3
Mathematical, Foundational and Computational Aspects of the Higher Infinite
http://sms.cam.ac.uk/collection/2054111
The goals of set theory are the analysis of the structure of the Higher Infinite, i.e. Cantor's settheoretic universe and the elucidation of the nature of infinite mathematical objects and their role in foundational issues underlying mathematics. Moreover, the current standard system of set theory, the ZermeloFraenkel axioms with the Axiom of Choice (ZFC), is the usual framework for a large part of mathematics.
Current settheoretic research on infinity focuses on the following three broad areas: large Cardinals and inner model theory, descriptive settheoretic methods and classification problems, and infinite combinatorics.
The programme HIF will connect these three main strands of settheoretic research and other fields of set theory to the wider scope of mathematics, to research in the foundations of mathematics, including some philosophical issues, and to research on computational issues of infinity, e.g. in theoretical computer science and constructive mathematics.
The following topics are a nonexclusive list of important examples of relevant fields for the research done in the programme HIF:
1.The structure of definable subsets of the continuum
2.Infinite combinatorics, forcing, and large cardinals
3.Inner models of large cardinals and aspects of determinacy
4.Applications of set theory to other areas of mathematics
5.Constructive set theory and new models of computation
6.Set theory and the foundations of mathematics
Three workshops are planned during the programme: The first one (2428 August 2015) will be the 5th European Set Theory Conference. The second workshop, entitled "New challenges in iterated forcing" will be a Satellite Meeting held at the University of East Anglia in Norwich (26 November 2015). A final workshop will take place on 1418 December 2015.
1440
2023
Tue, 14 Mar 2023 11:29:32 +0000
Tue, 25 Aug 2015 17:16:09 +0100
en
smssupport@uis.cam.ac.uk
Mathematical, Foundational and Computational Aspects of the Higher Infinite
http://sms.cam.ac.uk/collection/2054111
http://rss.sms.cam.ac.uk/itunesimage/2054112.jpg
http://video.search.yahoo.com/mrss
Mathematical, Foundational and Computational Aspects of the Higher Infinite
The goals of set theory are the analysis of the structure of the Higher Infinite, i.e. Cantor's settheoretic universe and the elucidation of the nature of infinite mathematical objects and their role in foundational issues underlying mathematics. Moreover, the current standard system of set theory, the ZermeloFraenkel axioms with the Axiom of Choice (ZFC), is the usual framework for a large part of mathematics.
Current settheoretic research on infinity focuses on the following three broad areas: large Cardinals and inner model theory, descriptive settheoretic methods and classification problems, and infinite combinatorics.
The programme HIF will connect these three main strands of settheoretic research and other fields of set theory to the wider scope of mathematics, to research in the foundations of mathematics, including some philosophical issues, and to research on computational issues of infinity, e.g. in theoretical computer science and constructive mathematics.
The following topics are a nonexclusive list of important examples of relevant fields for the research done in the programme HIF:
1.The structure of definable subsets of the continuum
2.Infinite combinatorics, forcing, and large cardinals
3.Inner models of large cardinals and aspects of determinacy
4.Applications of set theory to other areas of mathematics
5.Constructive set theory and new models of computation
6.Set theory and the foundations of mathematics
Three workshops are planned during the programme: The first one (2428 August 2015) will be the 5th European Set Theory Conference. The second workshop, entitled "New challenges in iterated forcing" will be a Satellite Meeting held at the University of East Anglia in Norwich (26 November 2015). A final workshop will take place on 1418 December 2015.
Mathematical, Foundational and Computational Aspects of the Higher Infinite
The goals of set theory are the analysis of the structure of the Higher Infinite, i.e. Cantor's settheoretic universe and the elucidation of the nature of infinite mathematical objects and their role in foundational issues underlying mathematics. Moreover, the current standard system of set theory, the ZermeloFraenkel axioms with the Axiom of Choice (ZFC), is the usual framework for a large part of mathematics.
Current settheoretic research on infinity focuses on the following three broad areas: large Cardinals and inner model theory, descriptive settheoretic methods and classification problems, and infinite combinatorics.
The programme HIF will connect these three main strands of settheoretic research and other fields of set theory to the wider scope of mathematics, to research in the foundations of mathematics, including some philosophical issues, and to research on computational issues of infinity, e.g. in theoretical computer science and constructive mathematics.
The following topics are a nonexclusive list of important examples of relevant fields for the research done in the programme HIF:
1.The structure of definable subsets of the continuum
2.Infinite combinatorics, forcing, and large cardinals
3.Inner models of large cardinals and aspects of determinacy
4.Applications of set theory to other areas of mathematics
5.Constructive set theory and new models of computation
6.Set theory and the foundations of mathematics
Three workshops are planned during the programme: The first one (2428 August 2015) will be the 5th European Set Theory Conference. The second workshop, entitled "New challenges in iterated forcing" will be a Satellite Meeting held at the University of East Anglia in Norwich (26 November 2015). A final workshop will take place on 1418 December 2015.
Cambridge University
Vincenzo Abete
vincenzo.abete@newton.ac.uk
http://sms.cam.ac.uk/collection/2054111
Mathematical, Foundational and Computational Aspects of the Higher Infinite
20150825T17:16:09+01:00
INIMS
101092
no

Selfdetermined sets of sentences
ucs_sms_2054111_2082992
http://sms.cam.ac.uk/media/2082992
Selfdetermined sets of sentences
Rivello, E (Università degli Studi di Torino)
Wednesday 2nd September 2015  14:40 to 15:10
Tue, 06 Oct 2015 14:07:46 +0100
Isaac Newton Institute
Rivello, E
d22e3ef58d7e75aeeaa5e598a7be01a1
e696f27c83091fa63023125750810afb
cfe23ed6029d441e19e5364328345c92
fa190d43df90f8a10f754d48ed1bbbf0
Rivello, E (Università degli Studi di Torino)
Wednesday 2nd September 2015 ...
Rivello, E (Università degli Studi di Torino)
Wednesday 2nd September 2015  14:40 to 15:10
Cambridge University
1632
http://sms.cam.ac.uk/media/2082992
Selfdetermined sets of sentences
Rivello, E (Università degli Studi di Torino)
Wednesday 2nd September 2015  14:40 to 15:10
20151006T14:07:46+01:00
1632
2082992
true
16x9
false
no

Ultrafilters without ppoint quotients
ucs_sms_2054111_2060700
http://sms.cam.ac.uk/media/2060700
Ultrafilters without ppoint quotients
Goldstern, M (Technische Universität Wien)
Friday 28 August 2015, 10:0011:00
Wed, 02 Sep 2015 17:58:38 +0100
Isaac Newton Institute
Goldstern, M
8d169dd3a5d0117689fdd1006f18bb95
9675f5b80510e615c2f05b08ed82cc3e
7ad3b209cb599fb38db07e84a7254bd8
7949f90334ca7c09724388a3d2d214e2
Goldstern, M (Technische Universität Wien)
Friday 28 August 2015, 10:0011:00
Goldstern, M (Technische Universität Wien)
Friday 28 August 2015, 10:0011:00
Cambridge University
3354
http://sms.cam.ac.uk/media/2060700
Ultrafilters without ppoint quotients
Goldstern, M (Technische Universität Wien)
Friday 28 August 2015, 10:0011:00
A ppoint is a nonprincipal ultrafilter on the set N of natural numbers which has the property that for every countable family of filter sets there is a pseudointersection in the filter, i.e. a filter set which is almost contained in each set of the family. Equivalently, a ppoint is an element of the StoneCech remainder beta(N) minus N whose neighborhood filter is closed under countable intersections.
It is well known that ppoints "survive" various forcing iterations, that is: extending a universe V with certain forcing iterations P will result in a universe V' in which all (or at least: certain wellchosen) ppoints are still ultrafilter bases in the extension. This shows that the sentence "The continuum hypothesis is false, yet there are aleph1generated ultrafilters, namely: certain ppoints" is relatively consistent with ZFC.
In a joint paper with Diego Mejia and Saharon Shelah (still in progress) we construct ultrafilters on N which are, on the one hand, far away from being ppoints (there is no RudinKeisler quotient which is a ppoint), but on the other hand can survive certain forcing iterations adding reals but killing ppoints. This shows that nonCH is consistent with small ultrafilter bases AND the nonexistence of ppoints.
20150902T17:58:39+01:00
3354
2060700
true
16x9
false
no

101 Years of Modern Set Theory: Felix Hausdorff's "Foundations of Set Theory"
ucs_sms_2054111_2054113
http://sms.cam.ac.uk/media/2054113
101 Years of Modern Set Theory: Felix Hausdorff's "Foundations of Set Theory"
Koepke, P (Universität Bonn)
Monday 24 August 2015, 10:0011:00
Tue, 25 Aug 2015 17:49:17 +0100
108
108100
Isaac Newton Institute
Koepke, P
737c99c424727cba565120036a6a78b5
9a5a2db340a4c24ee58a8662a66d80f6
2e36657b929317ee2bc86a4d48bad2a2
e712e26a46d47e3d10274acea8f9ede7
Koepke, P (Universität Bonn)
Monday 24 August 2015, 10:0011:00
Koepke, P (Universität Bonn)
Monday 24 August 2015, 10:0011:00
Cambridge University
3514
http://sms.cam.ac.uk/media/2054113
101 Years of Modern Set Theory: Felix Hausdorff's "Foundations of Set Theory"
Koepke, P (Universität Bonn)
Monday 24 August 2015, 10:0011:00
Felix Hausdorff's 1914 monograph "Grundzüge der Mengenlehre" (Foundations of Set Theory) marks the beginning of modern set theory:
 it is the first comprehensive presentation of set theory as a mature and rich mathematical field, untroubled by philosophical worries about infinity and paradoxes;
 it introduces fundamental notions and theories that have been crucial for the further development of set theory and its applications, notably the axioms for topological spaces;
 even today, a considerable part of research in set theory has direct links to Hausdorff's work.
In my talk I shall describe Hausdorff's book and locate it in the history of set theory. I shall also present his views on the foundations of mathematics and set theory.
20160526T14:00:10+01:00
3514
2054113
true
16x9
false
no

A generalisation of closed unbounded sets
ucs_sms_2054111_2054127
http://sms.cam.ac.uk/media/2054127
A generalisation of closed unbounded sets
Brickhill, H (University of Bristol)
Monday 24 August 2015, 13:3014:00
Tue, 25 Aug 2015 17:36:25 +0100
Isaac Newton Institute
Brickhill, H
2cb5c6cf6f071fbe6f75d9f1cedacb3c
ed1707edd7f3e17ee8034f47fa4a9fde
04a49545248d78e284353e1ab51cd0bf
e6d334bfc8d500abd3eeac17b1b645f6
Brickhill, H (University of Bristol)
Monday 24 August 2015, 13:3014:00
Brickhill, H (University of Bristol)
Monday 24 August 2015, 13:3014:00
Cambridge University
1586
http://sms.cam.ac.uk/media/2054127
A generalisation of closed unbounded sets
Brickhill, H (University of Bristol)
Monday 24 August 2015, 13:3014:00
A generalisation of stationarity, associated with stationary reflection, was introduced in [1]. I give an alternative characterisation of these nstationary sets by defining a generalisation of closed unbounded (club) sets, so an nstationary set is defined in terms of these nclubs in the usual way. I will then look into what familiar properties of stationary and club sets will still hold in this more general setting, and explore the connection between these concepts and indescribable cardinals. Many of the simpler properties generalise completely, but for others we need an extra assumption. For instance to generalise the splitting property of stationary sets we have: If kappa is \ Pi1 n−1 indescribable, then any nstationary subset of κ is the union of kappa many pairwisedisjoint nstationary sets. In L these properties generalise straightforwardly as there any cardinal which admits an nstationary set is Pi1n−1 indescribable [1] .
If there is time I will also introduce a generalisation of ineffable cardinals and a weak ⋄ principal that is associated.
[1] J. Bagaria, M. Magidor, and H. Sakai. Reflection and indescribability in the constructible universe. Israel Journal of Mathematics, to appear (2012).
20150825T17:36:25+01:00
1586
2054127
true
16x9
false
no

A revision theory for typefree probability
ucs_sms_2054111_2141141
http://sms.cam.ac.uk/media/2141141
A revision theory for typefree probability
Campbell Moore, CJ (LudwigMaximiliansUniversität München)
Monday 14th December 2015  16:00 to 17:00
Mon, 21 Dec 2015 16:48:40 +0000
Isaac Newton Institute
Campbell Moore, CJ
b1b21fcfb80ee21f5dcb3ada2951bbbe
aea15a9282c8d7c1ec720bcd4903818d
4b7f23004652f018222b24a8c4c76cfa
2b757c0549f3d4e2c73e299606241674
Campbell Moore, CJ (LudwigMaximiliansUniversität München)
Monday 14th...
Campbell Moore, CJ (LudwigMaximiliansUniversität München)
Monday 14th December 2015  16:00 to 17:00
Cambridge University
3780
http://sms.cam.ac.uk/media/2141141
A revision theory for typefree probability
Campbell Moore, CJ (LudwigMaximiliansUniversität München)
Monday 14th December 2015  16:00 to 17:00
20151221T16:48:40+00:00
3780
2141141
true
16x9
false
no

A superDowker filter
ucs_sms_2054111_2059803
http://sms.cam.ac.uk/media/2059803
A superDowker filter
Cummings, JWR (Carnegie Mellon University)
Thursday 27 August 2015, 16:0017:00
Tue, 01 Sep 2015 16:30:46 +0100
Isaac Newton Institute
Cummings, JWR
683ff6a838113e68c50dfe950c06401a
61517b6984b3af405c2d1de1d1bd57d8
2af3178f682d34e11828fc28840ba622
437141dabf89cba9d1f87061593d38d4
Cummings, JWR (Carnegie Mellon University)
Thursday 27 August 2015, 16:0017:00
Cummings, JWR (Carnegie Mellon University)
Thursday 27 August 2015, 16:0017:00
Cambridge University
3565
http://sms.cam.ac.uk/media/2059803
A superDowker filter
Cummings, JWR (Carnegie Mellon University)
Thursday 27 August 2015, 16:0017:00
A superDowker filter is a filter F on a set X such that
1) For every sequence of Flarge sets there are x,y distinct with x in A_y and y in A_x
2) For every partition of X into two parts there exist a sequence as in 1) and a cell of the partition such that all pairs as in 1) lie in this cell
Building on work of Balogh and Gruenhage we show the consistency of the existence of a superDowker filter
20150901T16:30:46+01:00
3565
2059803
true
16x9
false
no

An Introduction to infinite matroids
ucs_sms_2054111_2142247
http://sms.cam.ac.uk/media/2142247
An Introduction to infinite matroids
Carmesin, J (University of Cambridge)
Thursday 17th December 2015  13:30 to 14:30
Wed, 23 Dec 2015 14:51:10 +0000
Isaac Newton Institute
Carmesin, J
341defc220ded47e74c53daef02aaf41
b7fed1007f2e56b9f75812497cbc4912
08098ece05568cdab613726f18ec8e7a
53cf6a56a1494438ad159e50b0f55cab
Carmesin, J (University of Cambridge)
Thursday 17th December 2015  13:30 to...
Carmesin, J (University of Cambridge)
Thursday 17th December 2015  13:30 to 14:30
Cambridge University
3448
http://sms.cam.ac.uk/media/2142247
An Introduction to infinite matroids
Carmesin, J (University of Cambridge)
Thursday 17th December 2015  13:30 to 14:30
For various questions in Infinite Graph Theory, matroids have turned out to be the right tool to tackle them. This introduction to infinite matroids will be selfcontained; in particular I will explain what a matroid is.
20151223T14:51:10+00:00
3448
2142247
true
16x9
false
no

Another proof of the JayneRogers theorem
ucs_sms_2054111_2142268
http://sms.cam.ac.uk/media/2142268
Another proof of the JayneRogers theorem
Miller, B (Universität Wien)
Friday 18th December 2015  10:00 to 11:00
Wed, 23 Dec 2015 14:57:13 +0000
Isaac Newton Institute
Miller, B
eb33d1454a3fc57100728ee680a37a95
a51c18f2c3e1bf026b9b3646b8a8403c
3725d5e43622602a16bfdf937544d1f6
491e89d466fd3f16ff9662e10a93ed14
Miller, B (Universität Wien)
Friday 18th December 2015  10:00 to 11:00
Miller, B (Universität Wien)
Friday 18th December 2015  10:00 to 11:00
Cambridge University
3720
http://sms.cam.ac.uk/media/2142268
Another proof of the JayneRogers theorem
Miller, B (Universität Wien)
Friday 18th December 2015  10:00 to 11:00
20151223T14:57:13+00:00
3720
2142268
true
16x9
false
no

Approximate Ramsey properties of Matrices
ucs_sms_2054111_2141127
http://sms.cam.ac.uk/media/2141127
Approximate Ramsey properties of Matrices
LopezAbad, J (Consejo Superior de Investigaciones Cientificas)
Monday 14th December 2015  13:30 to 14:30
Mon, 21 Dec 2015 16:40:19 +0000
Isaac Newton Institute
LopezAbad, J
5f9d94795c7b20d695c2a8d358f8d292
df4734a67ab9850e3e85110038e394a9
e939e2f991a7e90d0d422cdcac9cf313
38cb50ec73e7731c97ef7799b4bca253
LopezAbad, J (Consejo Superior de Investigaciones Cientificas)
Monday 14th...
LopezAbad, J (Consejo Superior de Investigaciones Cientificas)
Monday 14th December 2015  13:30 to 14:30
Cambridge University
3510
http://sms.cam.ac.uk/media/2141127
Approximate Ramsey properties of Matrices
LopezAbad, J (Consejo Superior de Investigaciones Cientificas)
Monday 14th December 2015  13:30 to 14:30
20151221T16:40:19+00:00
3510
2141127
true
16x9
false
no

Approximate Ramsey properties of matrices and finite dimensional normed spaces
ucs_sms_2054111_2103611
http://sms.cam.ac.uk/media/2103611
Approximate Ramsey properties of matrices and finite dimensional normed spaces
LopezAbad, J (ICMAT, Madrid)
Thursday 29th October 2015  15:00 to 16:00
Wed, 04 Nov 2015 17:21:11 +0000
Isaac Newton Institute
LopezAbad, J
8fdfc0095fb323089bf4cf04896211f9
ae343d3b04363a2609f11d9ad9738037
94cb10b9fe56771909671655cfee4a59
d395ea467ec3bb45d8bba4113f6b23a6
LopezAbad, J (ICMAT, Madrid)
Thursday 29th October 2015  15:00 to 16:00
LopezAbad, J (ICMAT, Madrid)
Thursday 29th October 2015  15:00 to 16:00
Cambridge University
3385
http://sms.cam.ac.uk/media/2103611
Approximate Ramsey properties of matrices and finite dimensional normed spaces
LopezAbad, J (ICMAT, Madrid)
Thursday 29th October 2015  15:00 to 16:00
Joint work with D. Bartosova and B. Mbombo
20151104T17:21:11+00:00
3385
2103611
true
16x9
false
no

Around the definability of mad families
ucs_sms_2054111_2054141
http://sms.cam.ac.uk/media/2054141
Around the definability of mad families
Törnquist, A D (Københavns Universitet)
Monday 24 August 2015, 15:0016:00
Tue, 25 Aug 2015 17:55:46 +0100
Isaac Newton Institute
Törnquist, A D
84a35a15bbb4f24576cf5a0bc5b77d89
61f23295d6083d903d55a6e379187819
fe1dfe95ab529901cb4036fe6aa80034
d9cfb3e8014e19f25db866f3ef3ac51b
Törnquist, A D (Københavns Universitet)
Monday 24 August 2015, 15:0016:00
Törnquist, A D (Københavns Universitet)
Monday 24 August 2015, 15:0016:00
Cambridge University
3385
http://sms.cam.ac.uk/media/2054141
Around the definability of mad families
Törnquist, A D (Københavns Universitet)
Monday 24 August 2015, 15:0016:00
I will talk about my new proof that there are no analytic infinite mad (maximal almost disjoint) families of subsets of ω, a result originally proved by A.D.R. Mathias in his famous "Happy Families" paper. The new proof motivates a proof that there are no infinite mad families in Solovay's model. If time permits, I will also talk about the differences between mad families of subsets of ω and other types of mad families, such as eventually different families of functions from ω to ω, and why these problems may be very different from the situation presented by mad families of subsets of ω.
20150825T17:55:46+01:00
3385
2054141
true
16x9
false
no

Aspects of generalizing the concept of strong measure zero
ucs_sms_2054111_2083056
http://sms.cam.ac.uk/media/2083056
Aspects of generalizing the concept of strong measure zero
Wohofsky, W (Technische Universität Wien)
Tuesday 29th September 2015  16:00 to 17:00
Tue, 06 Oct 2015 14:49:44 +0100
Isaac Newton Institute
Wohofsky, W
30091f1b329dd1ad127c42d921e290cb
c9646ac4e464b1f1ff373c4eedf8ed5e
95eb74083d7b1e9892fed4edc5e5ac98
18ee1fbaafa29e7b6f4da355db35b632
Wohofsky, W (Technische Universität Wien)
Tuesday 29th September 2015  16:00...
Wohofsky, W (Technische Universität Wien)
Tuesday 29th September 2015  16:00 to 17:00
Cambridge University
4140
http://sms.cam.ac.uk/media/2083056
Aspects of generalizing the concept of strong measure zero
Wohofsky, W (Technische Universität Wien)
Tuesday 29th September 2015  16:00 to 17:00
20151006T14:49:44+01:00
4140
2083056
true
16x9
false
no

Beyond the infinite: Rothschild Distinguished Visiting Professor Lecture
ucs_sms_2054111_2085123
http://sms.cam.ac.uk/media/2085123
Beyond the infinite: Rothschild Distinguished Visiting Professor Lecture
Woodin, H (Harvard University)
Monday 5th October 2015  16:00 to 17:00
Thu, 08 Oct 2015 17:08:57 +0100
Isaac Newton Institute
Woodin, H
e30aa1c57b83f539c775c3b97e477b60
5c9d9d2270721d56a2fe091b21f522f1
7f9aaea477337b8d44a50d43ea446b16
b7bbe6ce818ff8264a593eff0cd0d601
Woodin, H (Harvard University)
Monday 5th October 2015  16:00 to 17:00
Woodin, H (Harvard University)
Monday 5th October 2015  16:00 to 17:00
Cambridge University
3660
http://sms.cam.ac.uk/media/2085123
Beyond the infinite: Rothschild Distinguished Visiting Professor Lecture
Woodin, H (Harvard University)
Monday 5th October 2015  16:00 to 17:00
The modern mathematical story of infinity began in the period 187984 with a series of papers by Cantor that defined the fundamental framework of the subject. Within 40 years the key ZFC axioms for Set Theory were in place and the stage was set for the detailed development of transfinite mathematics, or so it seemed. However, in a completely unexpected development, Cohen showed in 1963 that even the most basic problem of Set Theory, that of Cantor's Continuum Hypothesis, was not solvable on the basis of the ZFC axioms.
The 50 years since Cohen's work has seen a vast development of Cohen's method and the realization that the occurrence of unsolvable problems is ubiquitous in Set Theory. This arguably challenges the very conception of Cantor on which Set Theory is based.
Thus a fundamental dilemma has emerged. On the one hand, the discovery, also over the last 50 years, of a rich hierarchy axioms of infinity seems to argue that Cantor's conception is fundamentally sound. But on the other hand, the developments of Cohen's method over this same period seem to strongly suggest there can be no preferred extension of the ZFC axioms to a system of axioms that can escape the ramifications of Cohen's method.
But this dilemma was itself based on a misconception and recent discoveries suggest there is a resolution.
20151008T17:08:57+01:00
3660
2085123
true
16x9
false
no

Borel Matchings and equidecompositions
ucs_sms_2054111_2142275
http://sms.cam.ac.uk/media/2142275
Borel Matchings and equidecompositions
Marks, A [CALTECH (California Institute of Technology)]
Friday 18th December 2015  11:30 to 12:30
Wed, 23 Dec 2015 14:56:55 +0000
Isaac Newton Institute
Marks, A
0bab04a6143ecb24937c8bedae724d1b
200c4198524eb15194c900d2ea077c96
6f4ad7589e5a3723a699370c08996c3f
945f6a266e7b3ef3d7cb1d57268f8a9b
Marks, A [CALTECH (California Institute of Technology)]
Friday 18th December...
Marks, A [CALTECH (California Institute of Technology)]
Friday 18th December 2015  11:30 to 12:30
Cambridge University
3547
http://sms.cam.ac.uk/media/2142275
Borel Matchings and equidecompositions
Marks, A [CALTECH (California Institute of Technology)]
Friday 18th December 2015  11:30 to 12:30
We discuss several results related to the question of when a Borel graph has a Borel matching. Here, the analogue of Hall's matching theorem fails, but there are positive results giving Borel matchings in several contexts if we are willing to discard null or meager sets. We also discuss some applications to geometrical paradoxes. This is joint work with Spencer Unger.
20151223T14:56:55+00:00
3547
2142275
true
16x9
false
no

Chain conditions, layered partial orders and weak compactness
ucs_sms_2054111_2059787
http://sms.cam.ac.uk/media/2059787
Chain conditions, layered partial orders and weak compactness
Lücke, PM (Universität Bonn)
Thursday 27 August 2015, 14:0014:30
Tue, 01 Sep 2015 16:17:23 +0100
Isaac Newton Institute
Lücke, PM
27cf12ba75a70f3899527e2bef42cf65
b2637d14ded09ba3324e1b04bb753f6b
16a60d975dd671da48bad7d4dddb141c
009912c61078b634ca7a07b8613ccc3f
Lücke, PM (Universität Bonn)
Thursday 27 August 2015, 14:0014:30
Lücke, PM (Universität Bonn)
Thursday 27 August 2015, 14:0014:30
Cambridge University
1699
http://sms.cam.ac.uk/media/2059787
Chain conditions, layered partial orders and weak compactness
Lücke, PM (Universität Bonn)
Thursday 27 August 2015, 14:0014:30
Motivated by a conjecture of Todorcevic, we study strengthenings of the κ−chain conditions that are equivalent to the κ−chain condition in the case where κ is a weakly compact cardinal. We then use such properties to provide new characterizations of weakly compact cardinals. In addition, we show that the question whether weak compactness is characterized by the statement that all κ−Knaster posets satisfy these properties is independent from the axioms of ZFC. This is joint work with Sean D. Cox (VCU Richmond).
20150901T16:17:23+01:00
1699
2059787
true
16x9
false
no

Cofinalities of Marczewski Ideals
ucs_sms_2054111_2059258
http://sms.cam.ac.uk/media/2059258
Cofinalities of Marczewski Ideals
Khomskii, Y (Universität Hamburg)
Wednesday 26 August 2015, 13:3014:00
Tue, 01 Sep 2015 12:05:26 +0100
Isaac Newton Institute
Khomskii, Y
dd1652343ecc916e11d79515e49864c8
733de25457825b88eafe128199ed1d2d
dcffeaace0377cdb0f0ece5e5c59f301
Khomskii, Y (Universität Hamburg)
Wednesday 26 August 2015, 13:3014:00
Khomskii, Y (Universität Hamburg)
Wednesday 26 August 2015, 13:3014:00
Cambridge University
1604
http://sms.cam.ac.uk/media/2059258
Cofinalities of Marczewski Ideals
Khomskii, Y (Universität Hamburg)
Wednesday 26 August 2015, 13:3014:00
We study the cofinality number of sigmaideals related to the Marczewskiideal on the Baire and Cantor space. These ideals are not Borelgenerated, and the cofinality number is usually greater than the continuum.
This is joint work with Jörg Brendle and Wolfgang Wohofsky.
20150901T12:05:27+01:00
1604
2059258
true
16x9
false
no

Computable analysis and games in descriptive set theory
ucs_sms_2054111_2090880
http://sms.cam.ac.uk/media/2090880
Computable analysis and games in descriptive set theory
Nobrega, H (Universiteit van Amsterdam)
Friday 9th October 2015  12:30 to 13:25
Fri, 16 Oct 2015 16:53:15 +0100
Isaac Newton Institute
Nobrega, H
6e0d2db42d5f5d9fc41f8240c365608b
3fb8a8159106b122e1f528748c537a88
9798a38beae088a8dd9179b75bd13768
e23c815e569d8b5e5b78028addef7761
Nobrega, H (Universiteit van Amsterdam)
Friday 9th October 2015  12:30 to...
Nobrega, H (Universiteit van Amsterdam)
Friday 9th October 2015  12:30 to 13:25
Cambridge University
2646
http://sms.cam.ac.uk/media/2090880
Computable analysis and games in descriptive set theory
Nobrega, H (Universiteit van Amsterdam)
Friday 9th October 2015  12:30 to 13:25
We report on ongoing work with Arno Pauly, showing how concepts from computable analysis can be used to shed light and uniformize certain games for classes of functions which have been studied in descriptive set theory, such as Wadge's game for continuous functions, Duparc's eraser game for Baire class 1 functions, and Semmes' tree game for Borel functions.
As an application, for each finite n we obtain a game characterizing the Baire class n of functions.
20151016T16:53:15+01:00
2646
2090880
true
16x9
false
no

Computing beyond Constructibility: The Recognizability Strength of Ordinal Time Machines
ucs_sms_2054111_2141210
http://sms.cam.ac.uk/media/2141210
Computing beyond Constructibility: The Recognizability Strength of Ordinal Time Machines
Carl, M (Universität Konstanz)
Wednesday 16th December 2015  13:30 to 14:30
Mon, 21 Dec 2015 16:59:16 +0000
Isaac Newton Institute
Carl, M
3b86d041459430e03159f41a7d89ca8d
3f7793a29533af79e67dada63fc677e2
0804227e025ad9ea54b1622a04f3742d
ba7ef3402369c6263e07cf27a5e355cf
Carl, M (Universität Konstanz)
Wednesday 16th December 2015  13:30 to 14:30
Carl, M (Universität Konstanz)
Wednesday 16th December 2015  13:30 to 14:30
Cambridge University
3463
http://sms.cam.ac.uk/media/2141210
Computing beyond Constructibility: The Recognizability Strength of Ordinal Time Machines
Carl, M (Universität Konstanz)
Wednesday 16th December 2015  13:30 to 14:30
Coauthor: Philipp Schlicht (Universität Bonn)
Transfinite machine models of computation provide an approach to an `effective mathematics of the uncountable'. However, their settheoretical interest seems to be limited by the fact that even the strongest such model, Koepke's Ordinal Turing Machines with parameters (pOTMs), can only compute constructible sets.
Recognizability is a more liberal notion than computability in that it only requires the machine to be able to identify a certain object when it is given to it as an input, not to produce that object.
By invoking notions from algorithmic randomness and considering recognizability rather than computability, we connect transfinite computability to large cardinals and forcing axioms incompatible with the axiom of constructibility on the one hand and inner models for large cardinals on the other. In particular, under appropriate large cardinal assumptions, a real number is heriditarily recognizable by a pOTM if and only if it is an element of the mouse for one Woodin cardinal. This is joint work with Philipp Schlicht.
20151221T16:59:16+00:00
3463
2141210
true
16x9
false
no

Connecting topological dimension theory and recursion theory
ucs_sms_2054111_2060686
http://sms.cam.ac.uk/media/2060686
Connecting topological dimension theory and recursion theory
Pauly, A (University of Cambridge)
Thursday 27 August 2015, 13:3014:00
Mon, 28 Sep 2015 13:57:39 +0100
Isaac Newton Institute
Pauly, A
946ee970b57daa11f36edd4951f988df
be7851ec3bb167a3a0c6824cea300116
3ae5f2f69fc60b6fc3c7edb15acedd37
5e2d60d78d5caca01fff045c84811be7
Pauly, A (University of Cambridge)
Thursday 27 August 2015, 13:3014:00
Pauly, A (University of Cambridge)
Thursday 27 August 2015, 13:3014:00
Cambridge University
1906
http://sms.cam.ac.uk/media/2060686
Connecting topological dimension theory and recursion theory
Pauly, A (University of Cambridge)
Thursday 27 August 2015, 13:3014:00
We introduce the point degree spectrum of a represented spaces as a substructure of the Medvedev degrees, which integrates the notion of Turing degrees, enumeration degrees, continuous degrees, and so on. The point degree spectrum connects descriptive set theory, topological dimension theory and computability theory. Through this new connection, for instance, we construct a family of continuum many infinite dimensional Cantor manifolds possessing Haver's property C whose Borel structures at an arbitrary finite rank are mutually nonisomorphic, which strengthen various theorems in infinite dimensional topology such as Roman Pol's solution to Pavel Alexandrov's old problem.
20150928T13:57:39+01:00
1906
2060686
true
16x9
false
no

Consecutively large families below the first inaccessible cardinal
ucs_sms_2054111_2103618
http://sms.cam.ac.uk/media/2103618
Consecutively large families below the first inaccessible cardinal
Brech, C (Universidade de São Paulo)
Thursday 29th October 2015  16:00 to 17:00
Wed, 04 Nov 2015 17:21:26 +0000
Isaac Newton Institute
Brech, C
266cad251243c9c2e448fe8fa92c05c7
1f3600d57f3dbe5d912d866e3d9a06eb
fe77e1e24f89b0f3164fdec3e4cef80a
3841913a289c57b9eb4220c35aaa2113
Brech, C (Universidade de São Paulo)
Thursday 29th October 2015  16:00 to...
Brech, C (Universidade de São Paulo)
Thursday 29th October 2015  16:00 to 17:00
Cambridge University
3292
http://sms.cam.ac.uk/media/2103618
Consecutively large families below the first inaccessible cardinal
Brech, C (Universidade de São Paulo)
Thursday 29th October 2015  16:00 to 17:00
20151104T17:21:26+00:00
3292
2103618
true
16x9
false
no

ContextDependent Deterministic Parallel Feedback Turing Computability
ucs_sms_2054111_2142240
http://sms.cam.ac.uk/media/2142240
ContextDependent Deterministic Parallel Feedback Turing Computability
Lubarsky, B (Florida Atlantic University)
Thursday 17th December 2015  11:30 to 12:30
Wed, 23 Dec 2015 14:49:43 +0000
Isaac Newton Institute
Lubarsky, B
da8462ccf1cc566ab5d1723f645f7a47
5c96e61c0e9d6e1f0867f227ec74929b
af05445fa7b2be0560ab2764d703fbc4
283a8fb538ec3e6fb14370652bd304c8
Lubarsky, B (Florida Atlantic University)
Thursday 17th December 2015  11:30...
Lubarsky, B (Florida Atlantic University)
Thursday 17th December 2015  11:30 to 12:30
Cambridge University
3660
http://sms.cam.ac.uk/media/2142240
ContextDependent Deterministic Parallel Feedback Turing Computability
Lubarsky, B (Florida Atlantic University)
Thursday 17th December 2015  11:30 to 12:30
The limit of this kind of computability is the least ordinal which is \Pi_1 gapreflecting on admissibles. If you would like to know what any of this means, come to the talk!
20151223T14:49:43+00:00
3660
2142240
true
16x9
false
no

Conway's funniest talk ever
ucs_sms_2054111_2118874
http://sms.cam.ac.uk/media/2118874
Conway's funniest talk ever
Conway, J H (Princeton University)
Thursday 19th November 2015  16:00 to 17:00
Wed, 25 Nov 2015 10:42:46 +0000
Isaac Newton Institute
Conway, J H
6f877c8fc4c5290636e5448bc50f51f5
4ca45304f9433232f9cd77f4adfeaf78
79c256a3d55ff742085e81350e6e57b3
75d5dbbcc68dafdf4b77d58437463354
Conway, J H (Princeton University)
Thursday 19th November 2015  16:00 to 17:00
Conway, J H (Princeton University)
Thursday 19th November 2015  16:00 to 17:00
Cambridge University
3840
http://sms.cam.ac.uk/media/2118874
Conway's funniest talk ever
Conway, J H (Princeton University)
Thursday 19th November 2015  16:00 to 17:00
20151125T10:42:46+00:00
3840
2118874
true
16x9
false
no

Delta_1definability of the nonstationary ideal
ucs_sms_2054111_2060714
http://sms.cam.ac.uk/media/2060714
Delta_1definability of the nonstationary ideal
Zdomskyy, L (Universität Wien)
Friday 28 August 2015, 11:3012:30
Wed, 02 Sep 2015 17:55:13 +0100
Isaac Newton Institute
Zdomskyy, L
24c1eac0f0b77a4fd333e112f147df77
bd6ce089dc8f477620cab762a4f46a6e
8d373a1b36e363af3707437c9fa177fe
a85dc8dc38713126982795dcbdf1f796
Zdomskyy, L (Universität Wien)
Friday 28 August 2015, 11:3012:30
Zdomskyy, L (Universität Wien)
Friday 28 August 2015, 11:3012:30
Cambridge University
2830
http://sms.cam.ac.uk/media/2060714
Delta_1definability of the nonstationary ideal
Zdomskyy, L (Universität Wien)
Friday 28 August 2015, 11:3012:30
The talk will be devoted to the proof of the fact that assuming V=L, for every successor cardinal κ there exists a GCH and cardinal preserving forcing poset P∈L such that in LP the ideal of all nonstationary subsets of κ is Δ1definable over H(κ+). We shall also discuss the situation for limit κ.
20150902T17:55:13+01:00
2830
2060714
true
16x9
false
no

Determinacy in Infinite Matroids
ucs_sms_2054111_2142254
http://sms.cam.ac.uk/media/2142254
Determinacy in Infinite Matroids
Bowler, N (Universität Hamburg)
Thursday 17th December 2015  14:45 to 15:45
Wed, 23 Dec 2015 14:51:39 +0000
Isaac Newton Institute
Bowler, N
2d667cd67cd70942aec008f1907d6aef
203a4c98a022f15fc389963e731eff31
e1966137bcbbdac1be3a66dd250df5a7
3618e2f89ffd7b1f9efa8c2797bdd04e
Bowler, N (Universität Hamburg)
Thursday 17th December 2015  14:45 to 15:45
Bowler, N (Universität Hamburg)
Thursday 17th December 2015  14:45 to 15:45
Cambridge University
3266
http://sms.cam.ac.uk/media/2142254
Determinacy in Infinite Matroids
Bowler, N (Universität Hamburg)
Thursday 17th December 2015  14:45 to 15:45
20151223T14:51:39+00:00
3266
2142254
true
16x9
false
no

Dual Ramsey theory on trees
ucs_sms_2054111_2103590
http://sms.cam.ac.uk/media/2103590
Dual Ramsey theory on trees
Todorcevic, S (CNRS, Paris and University of Toronto)
Tuesday 27th October 2015  15:00 to 16:00
Wed, 04 Nov 2015 17:15:44 +0000
Isaac Newton Institute
Todorcevic, S
9cbc5628a07d91d759a5a64d5e9567a8
e7eee6395db49ba5d46cc979e052d9cb
26555e43d19493f2b89767f8c6eaa7a6
15faaa43f37eaa82f2b328ad4405f100
Todorcevic, S (CNRS, Paris and University of Toronto)
Tuesday 27th October...
Todorcevic, S (CNRS, Paris and University of Toronto)
Tuesday 27th October 2015  15:00 to 16:00
Cambridge University
3339
http://sms.cam.ac.uk/media/2103590
Dual Ramsey theory on trees
Todorcevic, S (CNRS, Paris and University of Toronto)
Tuesday 27th October 2015  15:00 to 16:00
20151104T17:15:44+00:00
3339
2103590
true
16x9
false
no

Failures of the Forcing Theorem
ucs_sms_2054111_2059230
http://sms.cam.ac.uk/media/2059230
Failures of the Forcing Theorem
Holy, P (Universität Bonn)
Tuesday 25 August 2015, 16:0017:00
Tue, 01 Sep 2015 10:56:37 +0100
Isaac Newton Institute
Holy, P
ad3231d6713f9b1411281d5c5bb095ac
79bd60aaaf36c4ea28d1a52b49272462
b0790cf8f5b1e0dabb0622a98b5a81a9
50457c1ec25911bb4791fac334dc5f6d
Holy, P (Universität Bonn)
Tuesday 25 August 2015, 16:0017:00
Holy, P (Universität Bonn)
Tuesday 25 August 2015, 16:0017:00
Cambridge University
3316
http://sms.cam.ac.uk/media/2059230
Failures of the Forcing Theorem
Holy, P (Universität Bonn)
Tuesday 25 August 2015, 16:0017:00
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a condition in the relevant generic filter. We show that both the definability of the forcing relation and the truth lemma can fail for class forcing. We will also present positive results about and characterizations of the forcing theorem in class forcing. This is joint work with Regula Krapf, Philipp Lücke, Ana Njegomir and Philipp Schlicht.
20150901T10:56:37+01:00
3316
2059230
true
16x9
false
no

Forcing, regularity properties and the axiom of choice
ucs_sms_2054111_2059216
http://sms.cam.ac.uk/media/2059216
Forcing, regularity properties and the axiom of choice
Horowitz, H (Hebrew University of Jerusalem)
Tuesday 25 August 2015, 14:0014:30
Tue, 01 Sep 2015 09:34:18 +0100
Isaac Newton Institute
Horowitz, H
0dab02694e7bb2474c747e2348fdd3b8
4f60254458c8f20b9b17bc626af409d0
9059c6d33423d1504db2852651d67c7c
590fc0e1ebceb39192a1d6b4a8640797
Horowitz, H (Hebrew University of Jerusalem)
Tuesday 25 August 2015,...
Horowitz, H (Hebrew University of Jerusalem)
Tuesday 25 August 2015, 14:0014:30
Cambridge University
1152
http://sms.cam.ac.uk/media/2059216
Forcing, regularity properties and the axiom of choice
Horowitz, H (Hebrew University of Jerusalem)
Tuesday 25 August 2015, 14:0014:30
We consider general regularity properties associated with Suslin ccc forcing notions. By Solovay's celebrated work, starting from a model of ZFC+"There exists an inaccessible cardinal", we can get a model of ZF+DC+"All sets of reals are Lebesgue measurable and have the Baire property". By another famous result of Shelah, ZF+DC+"All sets of reals have the Baire property" is equiconsistent with ZFC. This result was obtained by isolating the notion of "sweetness", a strong version of ccc which is preserved under amalgamation, thus allowing the construction of a suitably homogeneous forcing notion.
The above results lead to the following question: Can we get a similar result for nonsweet ccc forcing notions without using an inaccessible cardinal?
In our work we give a positive answer by constructing a suitable ccc creature forcing and iterating along a nonwellfounded homogeneous linear order. While the resulting model satisfies ZF+¬ACω, we prove in a subsequent work that starting with a model of ZFC+"There is a measurable cardinal", we can get a model of ZF+DCω1. This is joint work with Saharon Shelah.
20150901T09:34:18+01:00
1152
2059216
true
16x9
false
no

Generic I0 at ℵω
ucs_sms_2054111_2059209
http://sms.cam.ac.uk/media/2059209
Generic I0 at ℵω
Dimonte, V (Universität Wien)
Tuesday 25 August 2015, 13:3014:00
Tue, 01 Sep 2015 09:36:52 +0100
Isaac Newton Institute
Dimonte, V
c968f5a79b019c5d7765f10a031dcf12
5b0cdb00c560f4d223c72adb9031198c
ee8ddc27901938433de104f625cf08fc
1ba2f7497cef3983c0c24770ec8cc27e
Dimonte, V (Universität Wien)
Tuesday 25 August 2015, 13:3014:00
Dimonte, V (Universität Wien)
Tuesday 25 August 2015, 13:3014:00
Cambridge University
1432
http://sms.cam.ac.uk/media/2059209
Generic I0 at ℵω
Dimonte, V (Universität Wien)
Tuesday 25 August 2015, 13:3014:00
It is common practice to consider the generic version of large cardinals defined with an elementary embedding, but what happens when such cardinals are really large? The talk will concern a form of generic I0 and the consequences of this extravagant hypothesis on the "largeness" of the powerset of ℵω. This research is a result of discussions with Hugh Woodin.
20150901T09:36:52+01:00
1432
2059209
true
16x9
false
no

Genius at Play: Reading, Talk, Q&A with John Horton Conway and Siobhan Roberts
ucs_sms_2054111_2118843
http://sms.cam.ac.uk/media/2118843
Genius at Play: Reading, Talk, Q&A with John Horton Conway and Siobhan Roberts
Conway, J H & Roberts, S
Monday 16th November 2015  15:00 to 16:30
Wed, 25 Nov 2015 10:50:21 +0000
Isaac Newton Institute
Conway, J H & Roberts, S
f1f4c6acddae58217d8468d90ec156f3
d622d525d440819ccefcb5af07d4f012
e3be4de30c5b2503da49e18772707c16
0328cd1187c74f37aad71fe4550963c7
Conway, J H & Roberts, S
Monday 16th November 2015  15:00 to 16:30
Conway, J H & Roberts, S
Monday 16th November 2015  15:00 to 16:30
Cambridge University
6360
http://sms.cam.ac.uk/media/2118843
Genius at Play: Reading, Talk, Q&A with John Horton Conway and Siobhan Roberts
Conway, J H & Roberts, S
Monday 16th November 2015  15:00 to 16:30
John Horton Conway, subject of the recently published book Genius At Play, will sit down with his (inadvertently authorized) biographer Siobhan Roberts and discusses the trials and tribulations of being biographized  the genesis of the project, the process over nearly a decade, and the challenge of looking back at the span of one's mathematical career. During what he calls his annus mirabilis at Cambridge in 1970, Conway discovered the Game of Life (with which he currently maintains a love/hate relationship), as well as the surreal numbers (of which he is proudest), and the Conway group. He recently celebrated the 30th anniversary of The ATLAS of Finite Groups. In 1986, he moved from Cambridge (where he was famous for his incessant game playing in the common room) to Princeton (where he became known for the same). Currently a professor emeritus at Princeton, Conway is now finally hard at work.
20151125T10:50:21+00:00
6360
2118843
true
16x9
false
no

Happy Families and Their Relatives
ucs_sms_2054111_2059769
http://sms.cam.ac.uk/media/2059769
Happy Families and Their Relatives
Halbeisen, L J (ETH Zürich)
Thursday 27 August 2015, 11:3012:30
Tue, 01 Sep 2015 16:26:33 +0100
Isaac Newton Institute
Halbeisen, L J
c7536c6c46d945a664f023a4833eb0ac
fe68d2ca37a76036b3ee5cf2552d10f1
b2d6e3af7ff57b7053581689c489d851
5d56116a145f8e9848fb2957b2ddb1a9
Halbeisen, L J (ETH Zürich)
Thursday 27 August 2015, 11:3012:30
Halbeisen, L J (ETH Zürich)
Thursday 27 August 2015, 11:3012:30
Cambridge University
3291
http://sms.cam.ac.uk/media/2059769
Happy Families and Their Relatives
Halbeisen, L J (ETH Zürich)
Thursday 27 August 2015, 11:3012:30
We first recall the notion of happy families as well as their combinatorial properties. Then we present some families which are related to happy families and investigate Mathias forcing restricted to these families. In the second part we show the relation between Mathias forcing and the Ramsey property and discuss the still open problem whether one can take Mathias′ inaccessible away. In the last part, we sketch Shelah's construction of a model of ZFC in which there are exactly 70 happy ultrafilters.
20150901T16:26:33+01:00
3291
2059769
true
16x9
false
no

Hyperclass Forcing in Morse Kelley Set Theory
ucs_sms_2054111_2059163
http://sms.cam.ac.uk/media/2059163
Hyperclass Forcing in Morse Kelley Set Theory
Antos, C (Universität Wien)
Monday 24 August 2015, 14:0014:30
Tue, 01 Sep 2015 09:07:32 +0100
Isaac Newton Institute
Antos, C
c493dab6b37cf309469a9c83cea1377d
7aa6e0a3e372d9bb4cc9a37a92b89ce1
00415b9c3d7143c1145111d6a3b69a2d
3d5348ad4997ac50476045fa30c30624
Antos, C (Universität Wien)
Monday 24 August 2015, 14:0014:30
Antos, C (Universität Wien)
Monday 24 August 2015, 14:0014:30
Cambridge University
1746
http://sms.cam.ac.uk/media/2059163
Hyperclass Forcing in Morse Kelley Set Theory
Antos, C (Universität Wien)
Monday 24 August 2015, 14:0014:30
There are mainly two different types: setforcing and classforcing, where the forcing notion is a set or class respectively. Here, we want to introduce and study the next step in this classification by size, namely hyperclassforcing (where the conditions of the forcing notion are themselves classes) in the context of an extension of MorseKelley class theory, called MK∗. We define this forcing by using a symmetry between MK∗ models and models of ZFC− plus there exists a strongly inaccessible cardinal (called SetMK∗). We develop a coding between βmodels M of MK∗ and transitive models M+ of SetMK∗ which will allow us to go from M to M+ and vice versa. So instead of forcing with a hyperclass in MK∗ we can force over the corresponding SetMK∗ model with a class of conditions. For classforcing to work in the context of ZFC− we show that the SetMK∗ model M+ can be forced to look like Lκ∗[X], where κ∗ is the height of M+, κ strongly inaccessible in M+ and X⊆κ. Over such a model we can apply classforcing and we arrive at an extension of M+ from which we can go back to the corresponding βmodel of MK∗, which will in turn be an extension of the original M. We conclude by giving an application of this forcing in sho wing that every βmodel of MK∗ can be extended to a minimal βmodel of MK∗ with the same ordinals.
20150901T09:07:32+01:00
1746
2059163
true
16x9
false
no

Inaccessible cardinals and accessible categories
ucs_sms_2054111_2141155
http://sms.cam.ac.uk/media/2141155
Inaccessible cardinals and accessible categories
Rosický, J (Masaryk University)
Tuesday 15th December 2015  11:30 to 12:30
Mon, 21 Dec 2015 16:52:11 +0000
Isaac Newton Institute
Rosický, J
598600f78383b007dc486190875c6c8b
f81a39355f53b0307ed6fae8ddb0bff4
657d7886202d7f51f62068c2c61c0b25
7b5a0481761246cc589778e9e4d29cb9
Rosický, J (Masaryk University)
Tuesday 15th December 2015  11:30 to 12:30
Rosický, J (Masaryk University)
Tuesday 15th December 2015  11:30 to 12:30
Cambridge University
3511
http://sms.cam.ac.uk/media/2141155
Inaccessible cardinals and accessible categories
Rosický, J (Masaryk University)
Tuesday 15th December 2015  11:30 to 12:30
There is a growing list of important questions in category theory, abstract homotopy theory or model theory where answers depend on large cardinals. These questions concern various properties of accessible categories which can be imagined as categories of models of infinitary first order theories. The answers depend on Vopenka's principle or its consequences, mostly on the existence of a proper class of suitable large cardinals. We will give examples of such questions, explain their characteristic features and mention open problems.
20151221T16:52:11+00:00
3511
2141155
true
16x9
false
no

Indestructible remarkable cardinals
ucs_sms_2054111_2060749
http://sms.cam.ac.uk/media/2060749
Indestructible remarkable cardinals
Gitman, V (City University of New York)
Friday 28 August 2015, 16:0017:00
Wed, 02 Sep 2015 18:14:36 +0100
Isaac Newton Institute
Gitman, V
5eb333040999bf38d216492c88f2288b
4d9c92ad27d256b6c3b47e82cac570bd
c0d7ade4f805e9f78c0f2830cb98a57d
f6c801515c9557467ffc40568a7da5c4
Gitman, V (City University of New York)
Friday 28 August 2015, 16:0017:00
Gitman, V (City University of New York)
Friday 28 August 2015, 16:0017:00
Cambridge University
3575
http://sms.cam.ac.uk/media/2060749
Indestructible remarkable cardinals
Gitman, V (City University of New York)
Friday 28 August 2015, 16:0017:00
In 2000, Schindler introduced remarkable cardinals and showed that the existence of a remarkable cardinal is equiconsistent with the assertion that the theory of L(R) is absolute for proper forcing. Remarkable cardinals can be thought of either as a miniature version of strong cardinals or as having aspects of generic supercompactness, but they are relatively low in the large cardinal hierarchy. They are downward absolute to L and lie (consistencywise) between the 1iterable and 2iterable cardinals of the αiterable cardinals hierarchy (below Ramsey cardinals). I will discuss the indestructibility properties of remarkable cardinals, which are similar to those of strong cardinals. I will show that a remarkable cardinal κ can be made simultaneously indestructible by all <κclosed ≤κdistributive forcing and by all forcing of the form Add(κ,θ)∗R, where R is forced to be <κclosed and ≤κdistributive. For this argument, I will introduce the notion of a remarkable Laver function and show that every remarkable cardinal has one. Although, the existence of Laverlike functions can be forced for most large cardinals, few, such as strong, supercompact, and extendible cardinals, have them outright. The established indestructibility can be used to show, for instance, that any consistent continuum pattern on the regular cardinals can be realized above a remarkable cardinal and that a remarkable cardinal need not be even weakly compact in HOD. This is joint work with Yong Cheng.
20150902T18:14:37+01:00
3575
2060749
true
16x9
false
no

Infinite dimensional Ellentuck spaces
ucs_sms_2054111_2060693
http://sms.cam.ac.uk/media/2060693
Infinite dimensional Ellentuck spaces
Dobrinen, NL (University of Denver)
Friday 28 August 2015, 09:0010:00
Wed, 02 Sep 2015 17:59:42 +0100
Isaac Newton Institute
Dobrinen, NL
c3e44a39799a02e64b3423124088ab0a
684ec2c4130a45b71584a275ea5ca962
13311fe3af6bdc3d3e53f5144d5114d2
9e19afcea719295597f5089709a699f6
Dobrinen, NL (University of Denver)
Friday 28 August 2015, 09:0010:00
Dobrinen, NL (University of Denver)
Friday 28 August 2015, 09:0010:00
Cambridge University
3600
http://sms.cam.ac.uk/media/2060693
Infinite dimensional Ellentuck spaces
Dobrinen, NL (University of Denver)
Friday 28 August 2015, 09:0010:00
Topological Ramsey spaces have proved essential to solving certain problems in Banach spaces, Graph Theory, Set Theory, and Topology. In recent years, they have provided a mechanism for investigating initial RudinKeisler and Tukey structures in the StoneCech compactification of the natural numbers. In work of Dobrinen and Todorcevic and work of Dobrinen, Mijares, Trujillo, certain partial orders which force ultrafilters with partition relations were found to be equivalent to some new classes of topological Ramsey spaces. These in turn were used to precisely investigate the Ramseytheoretic properties and the Tukey and RudinKeisler structures of the associated ultrafilters.
The Ellentuck space is the quintessential example of a topological Ramsey space. It is closely connected with Mathias forcing and with P(ω)/Fin which forces a Ramsey ultrafilter. Building on work in [Blass/Dobrinen/Raghavan15] investigating the Tukey type of the ultrafilter forced by P(ω×ω)/Fin⊗Fin, we found in [DobrinenJSL15] that the essential structure responsible for the forcing properties actually is a 2dimensional version of the Ellentuck space.
In this talk, we will present work in [DobrinenIDE15] constructing a new class of topological Ramsey spaces which may be viewed as infinite dimensional Ellentuck spaces. We will then present the Ramseyclassification theorems for equivalence relations on fronts and some applications to their related σclosed forcings and the RudinKeisler and Tukey structures below the generic ultrafilters.
[Blass/Dobrinen/Raghavan15] Andreas Blass, Natasha Dobrinen, and Dilip Raghavan, The next best thing to a ppoint, Journal of Symbolic Logic 80, no.3, 866900.
[DobrinenJSL15] Natasha Dobrinen, High dimensional Ellentuck spaces and initial chains in the Tukey structure of nonppoints, Journal of Symbolic Logic, 27pp, To appear.
[DobrinenIDE15] Natasha Dobrinen, Infinite dimensional Ellentuck spaces, 35 + pp, Preprint.
20150902T17:59:42+01:00
3600
2060693
true
16x9
false
no

Infinite Matroids and Pushdown Automata on Infinite Words
ucs_sms_2054111_2141196
http://sms.cam.ac.uk/media/2141196
Infinite Matroids and Pushdown Automata on Infinite Words
Wojciechowski, J (West Virginia University)
Wednesday 16th December 2015  11:30 to 12:00
Mon, 21 Dec 2015 16:45:21 +0000
Isaac Newton Institute
Wojciechowski, J
fd54d22b582504290617bcd0f9a2d8ac
141753f849378509967abd14de3a0373
0d4a254820b01c58f71100ba4961b6d9
cfb8220c3eb09f40c899dcd8f9df0c38
Wojciechowski, J (West Virginia University)
Wednesday 16th December 2015 ...
Wojciechowski, J (West Virginia University)
Wednesday 16th December 2015  11:30 to 12:00
Cambridge University
1891
http://sms.cam.ac.uk/media/2141196
Infinite Matroids and Pushdown Automata on Infinite Words
Wojciechowski, J (West Virginia University)
Wednesday 16th December 2015  11:30 to 12:00
The aim of this talk is to propose a topic of study that connects infinite matroids with pushdown automata on words indexed by arbitrary linear orders. The motivation for this study is the key open conjecture concerning infinite matroids, the Intersection Conjecture of NashWilliams, as well as a result from my paper "Infinite Matroidal Version of Hall's Matching Theorem, J. London Math. Soc., (2) 71 (2005), 563–578." The main result of this paper can be described using pushdown automata as follows. Let P=(M,W) be a pair of matroids on the same groundset E. We assign to P a language L_P consisting of transfinite words (indexed by ordinals) on the alphabet A={1,0,1}. The language L_P is obtained by taking all injective transfinite sequences of the elements of E and translating each such sequence f into a word of L_P. The translation involves replacing an element of f by 1, 0 or 1 depending on whether it is spanned by its predecessors in both, one or none of the matroids M and W.
Theorem There exists a pushdown automaton T on transfinite sequences in the alphabet A such that the language L_T consisting of words accepted by T has the following property: For every pair P of matroids satisfying property (*), the language L_P is a subset of L_T if and only if the pair P has a packing (the ground set E can be partitioned into sets E_M and E_N that are spanning in M and N, respectively).
The property (*) is that M is either finitary or a countable union of finite corank matroids and W is finitary.
20151221T16:45:21+00:00
1891
2141196
true
16x9
false
no

Linking set theory to economics
ucs_sms_2054111_2083048
http://sms.cam.ac.uk/media/2083048
Linking set theory to economics
Mathias, ARD (Université de La Réunion)
Thursday 17th September 2015  15:00 to 16:00
Tue, 06 Oct 2015 14:36:46 +0100
Isaac Newton Institute
Mathias, ARD
8a8949b1fe1254e80a3a615b3aae75bb
ca6bc63350094b217423cec2d7b33fb9
7fc3372b1f4f58df6fe11e8c1cbf02bf
0128badec7d5be6ecfb8630c6b738b74
Mathias, ARD (Université de La Réunion)
Thursday 17th September 2015  15:00...
Mathias, ARD (Université de La Réunion)
Thursday 17th September 2015  15:00 to 16:00
Cambridge University
3103
http://sms.cam.ac.uk/media/2083048
Linking set theory to economics
Mathias, ARD (Université de La Réunion)
Thursday 17th September 2015  15:00 to 16:00
20151006T14:36:46+01:00
3103
2083048
true
16x9
false
no

Local Ramsey Theory in abstract spaces
ucs_sms_2054111_2059195
http://sms.cam.ac.uk/media/2059195
Local Ramsey Theory in abstract spaces
Di Prisco, C A (Universidad de los Andes)
Tuesday 25 August 2015, 10:0011:00
Tue, 01 Sep 2015 10:09:16 +0100
Isaac Newton Institute
Di Prisco, C A
a57a9518c409c512474f6d60d067e528
0fcee8ac7996e551ca0a3322964c351f
4497d8a7fbbff55b24f60eb9a7a8fbe3
d05b905436c23ce0e93161bd111ea45f
Di Prisco, C A (Universidad de los Andes)
Tuesday 25 August 2015, 10:0011:00
Di Prisco, C A (Universidad de los Andes)
Tuesday 25 August 2015, 10:0011:00
Cambridge University
3228
http://sms.cam.ac.uk/media/2059195
Local Ramsey Theory in abstract spaces
Di Prisco, C A (Universidad de los Andes)
Tuesday 25 August 2015, 10:0011:00
We study the notion of semiselectiviy for coideals of the space of infinite sets of natural numbers, and propose a generalization to abstract Ramsey spaces. We also consider the corresponding forcing notions. Abstract Ramsey spaces in the sense of Todorcevic [1] provide a general framework that unifies several Ramsey type results.
[1] Todorcevic, S. Introduction to Ramsey spaces. Princeton University Press, 2010.
20150901T10:09:16+01:00
3228
2059195
true
16x9
false
no

Long and short recursive constructionscardinal invariants and parametrized diamonds
ucs_sms_2054111_2141217
http://sms.cam.ac.uk/media/2141217
Long and short recursive constructionscardinal invariants and parametrized diamonds
Hrusak, M [Universidad Nacional Autónoma de México (UNAM)]
Wednesday 16th December 2015  15:00 to 16:00
Mon, 21 Dec 2015 16:59:28 +0000
Isaac Newton Institute
Hrusak, M
162a42a984a35784a997c66e013fe500
914f8002b9f5d1be6fe62632018df515
8175ee582a44f801d855f56e5caa19b0
b5d59875e10a04ee82d565a3ad7b1c2d
Hrusak, M [Universidad Nacional Autónoma de México (UNAM)]
Wednesday 16th...
Hrusak, M [Universidad Nacional Autónoma de México (UNAM)]
Wednesday 16th December 2015  15:00 to 16:00
Cambridge University
3322
http://sms.cam.ac.uk/media/2141217
Long and short recursive constructionscardinal invariants and parametrized diamonds
Hrusak, M [Universidad Nacional Autónoma de México (UNAM)]
Wednesday 16th December 2015  15:00 to 16:00
20151221T16:59:28+00:00
3322
2141217
true
16x9
false
no

Mathias and Set Theory
ucs_sms_2054111_2059758
http://sms.cam.ac.uk/media/2059758
Mathias and Set Theory
Kanamori, A (Boston University)
Thursday 27 August 2015, 09:0010:00
Tue, 01 Sep 2015 16:26:42 +0100
Isaac Newton Institute
Kanamori, A
5c63f3d1e973630e1de10b61cb7ee091
1a5fc3e479ffc46a5eb43167fec629fa
124101b30a116fb8845a7e4353df4f61
5edef6921d475fa998ff6a1e3d80a05e
Kanamori, A (Boston University)
Thursday 27 August 2015, 09:0010:00
Kanamori, A (Boston University)
Thursday 27 August 2015, 09:0010:00
Cambridge University
3600
http://sms.cam.ac.uk/media/2059758
Mathias and Set Theory
Kanamori, A (Boston University)
Thursday 27 August 2015, 09:0010:00
On Mathias Day, the life work of Adrian Mathias in set theory will be surveyed and celebrated, in full range and extent.
20150901T16:26:42+01:00
3600
2059758
true
16x9
false
no

On ideal equal convergence
ucs_sms_2054111_2060721
http://sms.cam.ac.uk/media/2060721
On ideal equal convergence
Staniszewski, M (University of Gdansk)
Friday 28 August 2015, 13:3014:00
Wed, 02 Sep 2015 17:41:38 +0100
Isaac Newton Institute
Staniszewski, M
c103d6ee7081386ae7a3450c9fbffe29
e7fde26b0eec6aa3beeab84447951fbc
0397b852dd2180b54bf4b48fe5d423df
684373aa45c18d7aadbac5e69b19f110
Staniszewski, M (University of Gdansk)
Friday 28 August 2015, 13:3014:00
Staniszewski, M (University of Gdansk)
Friday 28 August 2015, 13:3014:00
Cambridge University
1873
http://sms.cam.ac.uk/media/2060721
On ideal equal convergence
Staniszewski, M (University of Gdansk)
Friday 28 August 2015, 13:3014:00
We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Cs\'{a}sz\'{a}r and Laczkovich. The independent, equivalent definition was introduced by Bukovsk{\'a}. She called it quasinormal convergence. We study relationships between ideal equal convergence and various kinds of ideal convergences of sequences of real functions.
We prove a characterization showing when the ideal pointwise convergence does not imply the ideal equal (aka quasinormal) convergence. The characterization is expressed in terms of a cardinal coefficient related to the bounding number. Furthermore we consider ideal version of the bounding number on sets from coideals.
20150902T17:41:38+01:00
1873
2060721
true
16x9
false
no

On relating strong type theories and set theories
ucs_sms_2054111_2141148
http://sms.cam.ac.uk/media/2141148
On relating strong type theories and set theories
Rathjen, M (University of Leeds)
Tuesday 15th December 2015  10:00 to 11:00
Mon, 21 Dec 2015 16:53:04 +0000
Isaac Newton Institute
Rathjen, M
acf3b5602046cff5982f203dee14c537
42368ed1d960fc9647c78266b285f42e
f4d475c0e67ff24b0ae5427906e7f2e9
530288d92e137b72c5aeecda37a66a39
Rathjen, M (University of Leeds)
Tuesday 15th December 2015  10:00 to 11:00
Rathjen, M (University of Leeds)
Tuesday 15th December 2015  10:00 to 11:00
Cambridge University
3960
http://sms.cam.ac.uk/media/2141148
On relating strong type theories and set theories
Rathjen, M (University of Leeds)
Tuesday 15th December 2015  10:00 to 11:00
There exists a fairly tight fit between type theories à la MartinLöf and constructive set theories such as CZF and its extension, and there are connections to classical KripkePlatek set theory and extensions thereof, too. The technology for determining the (exact) prooftheoretic strength of such theories was developed in the late 20th century. The situation is rather different when it comes to type theories (with universes) having the impredicative type of propositions Prop from the Calculus of Constructions that features in some powerful proof assistants. Aczel's setsastypes interpretation into these type theories gives rise to rather unusual settheoretic axioms: negative power set and negative separation. But it is not known how to determine the consistency strength of intuitionistic set theories with such axioms via familiar classical set theories (though it is not difficult to see that ZFC plus infinitely many inaccessibles provides an upper bound). The first part of the talk will be a survey of known results from this area. The second part will be concerned with the rather special computational and prooftheoretic behavior of such theories.
20151221T16:53:04+00:00
3960
2141148
true
16x9
false
no

On the class of perfectly null sets and its transitive version
ucs_sms_2054111_2059251
http://sms.cam.ac.uk/media/2059251
On the class of perfectly null sets and its transitive version
Korch, M (Uniwersytet Warszawski)
Wednesday 26 August 2015, 14:0014:30
Tue, 01 Sep 2015 09:56:17 +0100
Isaac Newton Institute
Korch, M
4b197d3a15aba07f08ee2cf3cb43590c
293804f72cf2060dda7bc6c5d42dbeb3
e4cb91f95b05a1bd86d92e753f564e82
e883868a39461b4e24c835d14b8f4a3c
Korch, M (Uniwersytet Warszawski)
Wednesday 26 August 2015, 14:0014:30
Korch, M (Uniwersytet Warszawski)
Wednesday 26 August 2015, 14:0014:30
Cambridge University
1637
http://sms.cam.ac.uk/media/2059251
On the class of perfectly null sets and its transitive version
Korch, M (Uniwersytet Warszawski)
Wednesday 26 August 2015, 14:0014:30
The ideals of universally null sets (UN, sets which are null with respect to any Borel diffused measure) and perfectly meager sets (PM, sets which are meager when restricted to any perfect set) are best known among the classes of special subsets of the real line. Those two ideals were long considered to be somehow dual, though some differences were also known. P. Zakrzewski proved that two other earlier defined classes of sets smaller then PM coincide and are dual to UN. Therefore he proposed to call this class universally meager sets. The PM class was left without a counterpart, and we try to define a class of sets which may play the role of a dual class to PM and we also consider its transitive version. I will present some properties of those classes and give few important problems which are still open.
20150901T09:56:17+01:00
1637
2059251
true
16x9
false
no

On the width of wqos
ucs_sms_2054111_2083070
http://sms.cam.ac.uk/media/2083070
On the width of wqos
Dzamonja, M (University of East Anglia)
Thursday 10th September 2015  15:00 to 16:00
Tue, 06 Oct 2015 14:45:04 +0100
Isaac Newton Institute
Dzamonja, M
e884dfb110efd01a30ab3d0a7918b194
f357d986535d339f98706cd7e89c05b3
a3c4f31a659a64147331378f45b3bdf2
b00ba6707dc1da4e594dd3cda7f5903b
Dzamonja, M (University of East Anglia)
Thursday 10th September 2015  15:00...
Dzamonja, M (University of East Anglia)
Thursday 10th September 2015  15:00 to 16:00
Cambridge University
3181
http://sms.cam.ac.uk/media/2083070
On the width of wqos
Dzamonja, M (University of East Anglia)
Thursday 10th September 2015  15:00 to 16:00
20151006T14:45:04+01:00
3181
2083070
true
16x9
false
no

On two problems on Boolean algebras and finitely additive measures
ucs_sms_2054111_2117683
http://sms.cam.ac.uk/media/2117683
On two problems on Boolean algebras and finitely additive measures
Plebanek, G (Uniwersytet Wrocławski)
Tuesday 10th November 2015  15:00 to 16:00
Mon, 23 Nov 2015 16:50:02 +0000
Isaac Newton Institute
Plebanek, G
f61315bd2a984c883f234ef458c5f5dd
775e2b5c00c3baf43456bd1a28b761cd
8b35a324bba07026c7b95d93f9f492c9
441b697280708805dcf93e637b0e1db8
Plebanek, G (Uniwersytet Wrocławski)
Tuesday 10th November 2015  15:00 to...
Plebanek, G (Uniwersytet Wrocławski)
Tuesday 10th November 2015  15:00 to 16:00
Cambridge University
3504
http://sms.cam.ac.uk/media/2117683
On two problems on Boolean algebras and finitely additive measures
Plebanek, G (Uniwersytet Wrocławski)
Tuesday 10th November 2015  15:00 to 16:00
20151123T16:50:02+00:00
3504
2117683
true
16x9
false
no

Order types of chains of Borel sets and Baire functions
ucs_sms_2054111_2103597
http://sms.cam.ac.uk/media/2103597
Order types of chains of Borel sets and Baire functions
Elekes, M (Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences)
Tuesday 27th October 2015  16:00 to 17:00
Wed, 04 Nov 2015 17:19:12 +0000
Isaac Newton Institute
Elekes, M
ed8a9d3df80a6cb7553332a307d8e149
52bac719dc04eb0c37f9b46cb7e3713e
c784a5a486cddc6ab9f91b2c11fd3785
129a4889ac3e49603dba8578c19a5852
Elekes, M (Alfréd Rényi Institute of Mathematics,Hungarian Academy of...
Elekes, M (Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences)
Tuesday 27th October 2015  16:00 to 17:00
Cambridge University
3579
http://sms.cam.ac.uk/media/2103597
Order types of chains of Borel sets and Baire functions
Elekes, M (Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences)
Tuesday 27th October 2015  16:00 to 17:00
20151104T17:19:12+00:00
3579
2103597
true
16x9
false
no

Pairwise Sums in the Reals
ucs_sms_2054111_2142261
http://sms.cam.ac.uk/media/2142261
Pairwise Sums in the Reals
Leader, I (University of Cambridge)
Thursday 17th December 2015  16:00 to 17:00
Wed, 23 Dec 2015 14:51:37 +0000
Isaac Newton Institute
Leader, I
527244fcd550b572c37dcd0fd3f14c5a
fbeb71687c5fb90dd41b9aeb60cc85cc
9d488016252e9780cfa4a1ede4df7222
5bdeeeec2d367be36d432fb1033426e6
Leader, I (University of Cambridge)
Thursday 17th December 2015  16:00 to...
Leader, I (University of Cambridge)
Thursday 17th December 2015  16:00 to 17:00
Cambridge University
3046
http://sms.cam.ac.uk/media/2142261
Pairwise Sums in the Reals
Leader, I (University of Cambridge)
Thursday 17th December 2015  16:00 to 17:00
Coauthors: Neil Hindman (Howard University), Dona Strauss (University of Leeds)
We show (assuming CH) that there is a finite colouring of the reals such that no infinite set X has X+X (meaning the pairwise sums from X, allowing repetition) monochromatic. And we give positive results for ‘nice’ colourings.
20151223T14:51:37+00:00
3046
2142261
true
16x9
false
no

Partition Relation Equiconsistent with ∃κ(o(κ)=κ+)
ucs_sms_2054111_2059276
http://sms.cam.ac.uk/media/2059276
Partition Relation Equiconsistent with ∃κ(o(κ)=κ+)
Kimchi, YM (Technion  Israel Institute of Technology)
Wednesday 26 August 2015, 14:0014:30
Tue, 01 Sep 2015 12:08:35 +0100
Isaac Newton Institute
Kimchi, YM
febf790a017eecedb48f01c750f188f3
3f8dcd6f28be884f8e98573b660fd3f1
d58b609526b7f55caef613e3a68d8c6e
02c36d05f6782fc4c09aa8c1f1526bcd
Kimchi, YM (Technion  Israel Institute of Technology)
Wednesday 26 August...
Kimchi, YM (Technion  Israel Institute of Technology)
Wednesday 26 August 2015, 14:0014:30
Cambridge University
1973
http://sms.cam.ac.uk/media/2059276
Partition Relation Equiconsistent with ∃κ(o(κ)=κ+)
Kimchi, YM (Technion  Israel Institute of Technology)
Wednesday 26 August 2015, 14:0014:30
Preamble: In this work we deal with partition relations with infinite exponents under ZFC, hence all results are limited to definable functions.
In [78], M. Spector has proven, basically, that ∃κ(o(κ)=1) is equiconsistent with ℵ1→(ω)ωℵ0. In [87], we were able to show that the result generalizes to n=2; namely, ∃κ(o(κ)=2) is equiconsistent with ℵ1→(ω2)ω2ℵ0. Surprisingly at first sight, this property cannot be generalized further (for n>2), and later on we were able to prove that ℵ1→(ω3)ω3ℵ0 is equiconsistent with ∃κ(o(o(κ))=2).
The above lead us to a finer notion of homogeneity:
Definition: Weak Homogeneity is the partition property κ−→−−−−\tiny WH(λ)ημ where the only considered subsequences of λ are those that are created by removing (or, complementarily, collecting) only finitely many segments of λ.
Using week homogeneity we were able to prove the following for any ordinal α [87]: ∃κ(o(κ)=α) is equiconsistent with ℵ1−→−−−−\tiny WH(ωα)ωαℵ0.
Later on we were able to characterize the consistency strength of ∃κ(o(κ) = κ), and recently we have arrived at the main result of this paper:
∃κ(o(κ)=κ+) is equiconsistent with ℵ1−→−−−−\tiny WH(ℵ1)ℵ1ℵ0
References:
[78] M. Spector: Natural Sentences of Mathematics which are independent of V=L, V=Lμ etc., 1978 (preprint).
[87] Y.M. Kimchi: Dissertation, 1987, The Hebrew University of Jerusalem, Israel
20150901T12:08:35+01:00
1973
2059276
true
16x9
false
no

Partition Relation Perspectives
ucs_sms_2054111_2141169
http://sms.cam.ac.uk/media/2141169
Partition Relation Perspectives
Larson, J (University of Florida)
Tuesday 15th December 2015  14:45 to 15:45
Mon, 21 Dec 2015 16:44:02 +0000
Isaac Newton Institute
Larson, J
9830189dea25c6e7bf9e3efa032e4046
aaabaf87f0ca1f3b15cf519719780cca
1458cdbb588dcdafc7955258de004cdb
d6574a49e2a229e120789fe617240449
Larson, J (University of Florida)
Tuesday 15th December 2015  14:45 to 15:45
Larson, J (University of Florida)
Tuesday 15th December 2015  14:45 to 15:45
Cambridge University
2561
http://sms.cam.ac.uk/media/2141169
Partition Relation Perspectives
Larson, J (University of Florida)
Tuesday 15th December 2015  14:45 to 15:45
We will look at partition relations from various perspectives, and discuss recent results and open problems.
20151221T16:44:02+00:00
2561
2141169
true
16x9
false
no

Prikry type sequences: a composition of interconnected results
ucs_sms_2054111_2059794
http://sms.cam.ac.uk/media/2059794
Prikry type sequences: a composition of interconnected results
Fuchs, G (City University of New York)
Thursday 27 August 2015, 15:0016:00
Tue, 01 Sep 2015 16:30:14 +0100
Isaac Newton Institute
Fuchs, G
d973d3effa53a2a5502ed74766a11067
65699646efaf886abadfe02bae28ed58
fa7e3590aec7b40afc8113e44375b0c8
08b46f9da75edcd712a3aa6f79b8a17e
Fuchs, G (City University of New York)
Thursday 27 August 2015, 15:0016:00
Fuchs, G (City University of New York)
Thursday 27 August 2015, 15:0016:00
Cambridge University
3562
http://sms.cam.ac.uk/media/2059794
Prikry type sequences: a composition of interconnected results
Fuchs, G (City University of New York)
Thursday 27 August 2015, 15:0016:00
I would like to survey a series of beautiful and almost mysterious properties of Prikry sequences which have analogues for other Prikry type forcings. The first of these is Mathias' characterization of Prikry sequences as those that are almost contained in every set of measure 1 with respect to the normal ultrafilter being used for the forcing. This is the key to the second property, which is that the sequence of critical points when forming iterated ultrapowers by that ultrafilter is a Prikry sequence over the limit model. Using this, it is not hard to conclude that Prikry sequences are maximal, in the sense that they almost contain every other Prikry sequence present in their forcing extension. Another phenomenon is that the forcing extension of the limit model by the critical sequence is the same as the intersection of the finite iterates. I will show another canonical representation of that model. Yet another property is that the limit model can be realized as a single Boolean ultrapower. Most of these results were known for Prikry forcing, and I will show that some of them carry over to certain variants of Prikry forcing and Magidor forcing.
20150901T16:30:14+01:00
3562
2059794
true
16x9
false
no

Ramsey Determinacy of adversarial Gowers games
ucs_sms_2054111_2103604
http://sms.cam.ac.uk/media/2103604
Ramsey Determinacy of adversarial Gowers games
de Rancourt, N (Université Paris 7  DenisDiderot)
Wednesday 28th October 2015  11:00 to 12:00
Wed, 04 Nov 2015 17:21:22 +0000
Isaac Newton Institute
de Rancourt, N
f6511fd5a2213be75a1d06a8eda1cf83
d46a5798ca6e8d9ada44fa444ba209a5
02e65233267e02c0d0c8cfd2c492c084
7ddf4429757a547fb2a81245d9d76f83
de Rancourt, N (Université Paris 7  DenisDiderot)
Wednesday 28th October...
de Rancourt, N (Université Paris 7  DenisDiderot)
Wednesday 28th October 2015  11:00 to 12:00
Cambridge University
3600
http://sms.cam.ac.uk/media/2103604
Ramsey Determinacy of adversarial Gowers games
de Rancourt, N (Université Paris 7  DenisDiderot)
Wednesday 28th October 2015  11:00 to 12:00
20151104T17:21:22+00:00
3600
2103604
true
16x9
false
no

Ramsey theory in topological dynamics
ucs_sms_2054111_2141113
http://sms.cam.ac.uk/media/2141113
Ramsey theory in topological dynamics
Bartosova, D (Universidade de São Paulo)
Monday 14th December 2015  10:00 to 11:00
Mon, 21 Dec 2015 16:20:29 +0000
Isaac Newton Institute
Bartosova, D
53d1587d74c4586fb2c40cff13dba5e2
edbf2966d5d862e9744337d73d8c53e5
9162a7553a6a6a0375b53ac41281e620
7fc037e72e45c9080b0de51ae456ab5a
Bartosova, D (Universidade de São Paulo)
Monday 14th December 2015  10:00 to...
Bartosova, D (Universidade de São Paulo)
Monday 14th December 2015  10:00 to 11:00
Cambridge University
3280
http://sms.cam.ac.uk/media/2141113
Ramsey theory in topological dynamics
Bartosova, D (Universidade de São Paulo)
Monday 14th December 2015  10:00 to 11:00
20151221T16:20:30+00:00
3280
2141113
true
16x9
false
no

Reversibility of Definable Relations
ucs_sms_2054111_2088706
http://sms.cam.ac.uk/media/2088706
Reversibility of Definable Relations
Kurilic, M (University of Novi Sad)
Tuesday 6th October 2015  15:00 to 16:00
Tue, 13 Oct 2015 16:45:42 +0100
Isaac Newton Institute
Kurilic, M
dc3c9ad84f85c04f04b4e48f7f5e0695
d8a525d7324bd11cd4c97fbe83f8a209
b505c22b5bbbda55b99e0cc133d656aa
c0caf91531c4d9a4f760d18f714b134d
Kurilic, M (University of Novi Sad)
Tuesday 6th October 2015  15:00 to 16:00
Kurilic, M (University of Novi Sad)
Tuesday 6th October 2015  15:00 to 16:00
Cambridge University
3720
http://sms.cam.ac.uk/media/2088706
Reversibility of Definable Relations
Kurilic, M (University of Novi Sad)
Tuesday 6th October 2015  15:00 to 16:00
20151013T16:45:42+01:00
3720
2088706
true
16x9
false
no

Selective properties of ideals
ucs_sms_2054111_2059780
http://sms.cam.ac.uk/media/2059780
Selective properties of ideals
Kwela, A (University of Gdansk)
Thursday 27 August 2015, 13:3014:00
Tue, 01 Sep 2015 16:15:21 +0100
Isaac Newton Institute
Kwela, A
9faea44ff9b01fdb5a051d4c259acd13
be3f5b4b9bf1d64a7c1c3e351ada8f8f
68371f12bcd4138252f362e7eed25f85
fa136d6d05f3760ea1c3ccdce76b6778
Kwela, A (University of Gdansk)
Thursday 27 August 2015, 13:3014:00
Kwela, A (University of Gdansk)
Thursday 27 August 2015, 13:3014:00
Cambridge University
1585
http://sms.cam.ac.uk/media/2059780
Selective properties of ideals
Kwela, A (University of Gdansk)
Thursday 27 August 2015, 13:3014:00
We will discuss several selective properties of ideals on countable sets. In the case of maximal ideals all those properties coincide and are equivalent to the notion of selectiveness of a maximal ideal (a maximal ideal is selective iff its dual filter is a Ramsey ultrafilter), however in general those selective properties differ from each other. We will show some of their connections to ideal convergence of sequences of functions, descriptive complexity of ideals and topological ways of representing ideals.
20150901T16:15:21+01:00
1585
2059780
true
16x9
false
no

Set theory and algebraic topology
ucs_sms_2054111_2142282
http://sms.cam.ac.uk/media/2142282
Set theory and algebraic topology
BrookeTaylor, A (University of Bristol)
Friday 18th December 2015  13:30 to 14:30
Wed, 23 Dec 2015 14:57:20 +0000
Isaac Newton Institute
BrookeTaylor, A
cc207e187b885b140a1f0717d2561a4a
0e656bf3db648c38b1d45895f9804eb8
f7a274c2b3e8318ee04f292081d0daff
1979db6b48c7b99626c4d7e30fa60bc7
BrookeTaylor, A (University of Bristol)
Friday 18th December 2015  13:30 to...
BrookeTaylor, A (University of Bristol)
Friday 18th December 2015  13:30 to 14:30
Cambridge University
3476
http://sms.cam.ac.uk/media/2142282
Set theory and algebraic topology
BrookeTaylor, A (University of Bristol)
Friday 18th December 2015  13:30 to 14:30
In this talk I plan to discuss some joint work with Sheila Miller related to knots. Quandles are algebraic structures that can be associated to (tame) knots, and they in fact constitute one of the few complete invariants we have for knots. However, there is some dissatisfaction with quandles as invariants, as it heuristically seems difficult to determine whether two quandles are isomorphic. Our result supports this impression: we show that the isomorphism relation of quandles is as complex as it possibly could be in Borel reducibility terms, being Borel complete. On the other hand, equivalence of tame knots is trivial from a Borel reducibility perspective, raising the prospect that more manageable complete invariants might exist.
20151223T14:57:21+00:00
3476
2142282
true
16x9
false
no

Singularizing Cardinals and Squarelike principles
ucs_sms_2054111_2141182
http://sms.cam.ac.uk/media/2141182
Singularizing Cardinals and Squarelike principles
Magidor, M (Hebrew University of Jerusalem)
Tuesday 15th December 2015  16:00 to 17:00
Mon, 21 Dec 2015 16:57:52 +0000
Isaac Newton Institute
Magidor, M
16a0ccae6e36836b0ed7eaaed9db7244
cda1d83d8f84923464aa1ac04400f72c
7ef480220a90eaf6f6b1c06a539a44b9
Magidor, M (Hebrew University of Jerusalem)
Tuesday 15th December 2015  16:00...
Magidor, M (Hebrew University of Jerusalem)
Tuesday 15th December 2015  16:00 to 17:00
Cambridge University
3840
http://sms.cam.ac.uk/media/2141182
Singularizing Cardinals and Squarelike principles
Magidor, M (Hebrew University of Jerusalem)
Tuesday 15th December 2015  16:00 to 17:00
20151221T16:57:53+00:00
3840
2141182
true
16x9
false
no

Strong Chang's Conjecture, SemiStationary Reflection, Strong Tree Property and Two Cardinal Square Principles
ucs_sms_2054111_2141120
http://sms.cam.ac.uk/media/2141120
Strong Chang's Conjecture, SemiStationary Reflection, Strong Tree Property and Two Cardinal Square Principles
TorresPerez, V (Technische Universität Wien)
Monday 14th December 2015  11:30 to 12:00
Mon, 21 Dec 2015 16:03:27 +0000
Isaac Newton Institute
TorresPerez, V
e61a807deab40d15b7f95d8bc8a0100e
3412b565985a5256455a780ed41ec41f
ed5742395eba88668e57964a11501435
6b052ee15e46fce65a0aafb041d9f676
TorresPerez, V (Technische Universität Wien)
Monday 14th December 2015 ...
TorresPerez, V (Technische Universität Wien)
Monday 14th December 2015  11:30 to 12:00
Cambridge University
1633
http://sms.cam.ac.uk/media/2141120
Strong Chang's Conjecture, SemiStationary Reflection, Strong Tree Property and Two Cardinal Square Principles
TorresPerez, V (Technische Universität Wien)
Monday 14th December 2015  11:30 to 12:00
We prove that the SemiStationary Reflection Principle, together with the negation of the Continuum Hypothesis, implies that ω2 has the Strong Tree Property. Also, we show that SSR implies the negation of □(λ,ω) for all regular cardinals λ≥ω2. This is a joint work with Liuzhen Wu.
20151221T16:03:27+00:00
1633
2141120
true
16x9
false
no

Symmetries
ucs_sms_2054111_2059223
http://sms.cam.ac.uk/media/2059223
Symmetries
Mota Gaytán, M A (Instituto Tecnológico Autónomo de México)
Tuesday 25 August 2015, 15:0016:00
Tue, 01 Sep 2015 10:46:07 +0100
Isaac Newton Institute
Mota Gaytán, M A
7f1a23b2452330abc5b554c1c02f2863
6cbc3b3a8bb57c0fe8d468754c5a3340
9314ad18502ba2a500f8b89a9b2132cf
53f7decbbb7c3e4f2df140cc6f8f49cf
Mota Gaytán, M A (Instituto Tecnológico Autónomo de México)
Tuesday 25 August...
Mota Gaytán, M A (Instituto Tecnológico Autónomo de México)
Tuesday 25 August 2015, 15:0016:00
Cambridge University
3180
http://sms.cam.ac.uk/media/2059223
Symmetries
Mota Gaytán, M A (Instituto Tecnológico Autónomo de México)
Tuesday 25 August 2015, 15:0016:00
In the last years there has been a second boom of the technique of forcing with side conditions (see for instance the recent works of AsperóMota, Krueger and Neeman describing three different perspectives of this technique). The first boom took place in the 1980s when Todorcevic discovered a method of forcing in which elementary substructures are included in the conditions of a forcing poset to ensure that the forcing poset preserves cardinals. More than twenty years later, Friedman and Mitchell independently took the first step in generalizing the method from adding small (of size at most the first uncountable cardinal) generic objects to adding larger objects by defining forcing posets with finite conditions for adding a club subset on the second uncountable cardinal. However, neither of these results show how to force (with side conditions together with another finite set of objects) the existence of such a large object together with the continuum being small. In the first part of this talk I will discuss new results in this area. This is joint work with John Krueger improving the symmetric CH preservation argument previously made by Asperó and Mota. In the second part of this talk I will use generalized symmetric systems in order to prove that, for each regular cardinal k, there is a poset Pk forcing the existence of a (k,k++)superatomic boolean algebra. This is joint work with William Weiss inspired in an unpublished note from September 2009 where Asperó and Bagaria introduced the forcing Pω.
20150901T10:46:07+01:00
3180
2059223
true
16x9
false
no

The higher sharp
ucs_sms_2054111_2060741
http://sms.cam.ac.uk/media/2060741
The higher sharp
Zhu, Y (Universität Münster)
Friday 28 August 2015, 15:0016:00
Wed, 02 Sep 2015 18:05:00 +0100
Isaac Newton Institute
Zhu, Y
25da07bc9b2d956cdcbf64758d8d1b1d
4daf2c2fcba0b89f414c967ca1d22d13
82269bd4961fb0bf35b9c00862d56297
c5737d85bce5a0724f752921f856c00a
Zhu, Y (Universität Münster)
Friday 28 August 2015, 15:0016:00
Zhu, Y (Universität Münster)
Friday 28 August 2015, 15:0016:00
Cambridge University
3192
http://sms.cam.ac.uk/media/2060741
The higher sharp
Zhu, Y (Universität Münster)
Friday 28 August 2015, 15:0016:00
We establish the descriptive set theoretic representation of the mouse M#n, which is called 0(n+1)#. At even levels, 0(2n)# is the higher level analog of Kleene's O; at odd levels, 0(2n+1)# is the unique iterable remarkable level(2n+1) blueprint.
20150902T18:05:00+01:00
3192
2060741
true
16x9
false
no

The Hurewicz dichotomy for generalized Baire spaces
ucs_sms_2054111_2054148
http://sms.cam.ac.uk/media/2054148
The Hurewicz dichotomy for generalized Baire spaces
Schlicht, P (Universität Bonn)
Monday 24 August 2015, 16:0017:00
Tue, 25 Aug 2015 17:50:00 +0100
Isaac Newton Institute
Schlicht, P
365964823152953edf30c857f25b0b32
410ca8b3bcc91fb2dc7ae33fe5e17b97
6f43c1db5dea155a8bda3bffeea1efd9
a9a37f5bd24957b96e59e9a8b56599fe
Schlicht, P (Universität Bonn)
Monday 24 August 2015, 16:0017:00
Schlicht, P (Universität Bonn)
Monday 24 August 2015, 16:0017:00
Cambridge University
2981
http://sms.cam.ac.uk/media/2054148
The Hurewicz dichotomy for generalized Baire spaces
Schlicht, P (Universität Bonn)
Monday 24 August 2015, 16:0017:00
By classical results of Hurewicz, Kechris and SaintRaymond, an analytic subset of a Polish space X is covered by a Ksigma subset of X if and only if it does not contain a closedinX subset homeomorphic to the Baire space omega^omega. We consider the analogous statement (which we call Hurewicz dichotomy) for Sigma11 subsets of the generalized Baire space kappa^kappa for a given uncountable cardinal kappa with kappa=kappa^(<kappa), and show how to force it to be true in a cardinal and cofinality preserving extension of the ground model. Moreover, we show that if the GCH holds, then there is a cardinal preserving class forcing extension in which the Hurewicz dichotomy for Sigma11 subsets of kappa^kappa holds at all uncountable regular cardinals kappa, while strongly unfoldable and supercompact cardinals are preserved. On the other hand, in the constructible universe L the dichotomy for Sigma11 sets fails at all uncountable regular cardinals, and the same happens in any generic extension obtained by adding a Cohen real to a model of GCH. This is joint work with Philipp Lücke and Luca Motto Ros.
20150825T17:50:00+01:00
2981
2054148
true
16x9
false
no

The Pinning Down Number and Cardinal Arithmetic
ucs_sms_2054111_2141162
http://sms.cam.ac.uk/media/2141162
The Pinning Down Number and Cardinal Arithmetic
Juhasz, I (Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences)
Tuesday 15th December 2015  13:30 to 14:30
Mon, 21 Dec 2015 16:51:24 +0000
Isaac Newton Institute
Juhasz, I
c0132f4e8fd7a32726ef41c3bf2a5974
481b0d117aa5182ff396d8dc5373d9a9
1f6948496e721a412e40462b6d3516ad
e7e96ef8505017b2f1344ec0d8091a6c
Juhasz, I (Alfréd Rényi Institute of Mathematics,Hungarian Academy of...
Juhasz, I (Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences)
Tuesday 15th December 2015  13:30 to 14:30
Cambridge University
3247
http://sms.cam.ac.uk/media/2141162
The Pinning Down Number and Cardinal Arithmetic
Juhasz, I (Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences)
Tuesday 15th December 2015  13:30 to 14:30
20151221T16:51:24+00:00
3247
2141162
true
16x9
false
no

The Search for Deep Inconsistency
ucs_sms_2054111_2059188
http://sms.cam.ac.uk/media/2059188
The Search for Deep Inconsistency
Koellner, P (Harvard University)
Tuesday 25 August 2015, 09:0010:00
Tue, 01 Sep 2015 10:17:00 +0100
Isaac Newton Institute
Koellner, P
ac25d81233e350e28e5f22fd116a00a0
e092e6d10f5dfdf81b5f73f80cec34b4
6639ae751760b4c1f79e76689dd45a4b
096e7c5913958c844e01c31155fdb8cd
Koellner, P (Harvard University)
Tuesday 25 August 2015, 09:0010:00
Koellner, P (Harvard University)
Tuesday 25 August 2015, 09:0010:00
Cambridge University
3535
http://sms.cam.ac.uk/media/2059188
The Search for Deep Inconsistency
Koellner, P (Harvard University)
Tuesday 25 August 2015, 09:0010:00
The hierarchy of large cardinals provides us with a canonical means to climb the hierarchy of consistency strength. There have been any purported inconsistency proofs of various large cardinal axioms. For example, there have been many proofs purporting to show that measurable cardinals are inconsistent. But to date the only proofs that have stood the test of time are those which are rather transparent and simple, the most notable example being Kunen's proof showing that Reinhardt cardinals are inconsistent. The Kunen result, however, makes use of AC. And long standing open question is whether Reinhardt cardinals are consistent in the context of ZF.
In this talk I will survey the simple inconsistency proofs and then raise the question of whether perhaps the large cardinal hierarchy outstrips AC, passing through Reinhardt cardinals and reaching far beyond. There are two main motivations for this investigation. First, it is of interest in its own right to determine whether the hierarchy of consistency strength outstrips AC. Perhaps there is an entire "choicless" large cardinal hierarchy, one which reaches new consistency strengths and has fruitful applications. Second, since the task of proving an inconsistency result becomes easier as one strengthens the hypothesis, in the search for a deep inconsistency it is reasonable to start with outlandishly strong large cardinal assumptions and then work ones way down. This will lead to the formulation of large cardinal axioms (in the context of ZF) that start at the level of a Reinhardt cardinal and pass upward through Berkeley cardinals (due to Woodin) and far beyond. Bagaria, Woodin, and myself have been charting out this new hierarchy. I will discuss what we have found so far.
20150901T10:17:00+01:00
3535
2059188
true
16x9
false
no

The size of conjugacy classes of automorphism groups
ucs_sms_2054111_2060728
http://sms.cam.ac.uk/media/2060728
The size of conjugacy classes of automorphism groups
Vidnyánszky, Z (Alfréd Rényi Institute of Mathematics)
Friday 28 August 2015, 14:0014:30
Wed, 02 Sep 2015 17:41:38 +0100
Isaac Newton Institute
Vidnyánszky, Z
fdcd2c339434c0b1a605a89cff895025
52d74365894578b6357f86540714373a
54ee9bcf723c47b17cff7cf134e54bf8
08f0bfc8b01a895e6266d379b75c4ca7
Vidnyánszky, Z (Alfréd Rényi Institute of Mathematics)
Friday 28 August 2015,...
Vidnyánszky, Z (Alfréd Rényi Institute of Mathematics)
Friday 28 August 2015, 14:0014:30
Cambridge University
1655
http://sms.cam.ac.uk/media/2060728
The size of conjugacy classes of automorphism groups
Vidnyánszky, Z (Alfréd Rényi Institute of Mathematics)
Friday 28 August 2015, 14:0014:30
The automorphism groups of Fraissé limits are usually interesting objects both from group theoretic and set theoretic viewpoint. However, these groups are often nonlocally compact, hence there is no natural translation invariant measure on them. Christensen introduced the notion of Haar null sets in nonlocally compact Polish groups which is a wellbehaved generalisation of the null ideal to such groups. In my talk I will present some new results concerning the size of the conjugacy classes of automorphism groups of Fraisse limits with respect to this notion.
20150902T17:41:38+01:00
1655
2060728
true
16x9
false
no

The surreal numbers
ucs_sms_2054111_2118858
http://sms.cam.ac.uk/media/2118858
The surreal numbers
Conway, J H (Princeton University)
Thursday 19th November 2015  15:00 to 16:00
Wed, 25 Nov 2015 10:39:50 +0000
Isaac Newton Institute
Conway, J H
1f115c519c92697536c041359dcc45e5
c12a4ea82c0f509341da2e08692f627a
b16d1551a16976fd4d7fb5d4e5807437
5db64e7d93a55c206d942355ccc538ce
Conway, J H (Princeton University)
Thursday 19th November 2015  15:00 to 16:00
Conway, J H (Princeton University)
Thursday 19th November 2015  15:00 to 16:00
Cambridge University
3571
http://sms.cam.ac.uk/media/2118858
The surreal numbers
Conway, J H (Princeton University)
Thursday 19th November 2015  15:00 to 16:00
20151125T10:39:51+00:00
3571
2118858
true
16x9
false
no

The tree property (session 1)
ucs_sms_2054111_2054120
http://sms.cam.ac.uk/media/2054120
The tree property (session 1)
Sinapova, D (University of Illinois at Chicago)
Monday 24 August 2015, 11:3012:30
Tue, 25 Aug 2015 17:55:36 +0100
Isaac Newton Institute
Sinapova, D
5ad62cc9f9f6093f7e994c2e41e794cd
876ed2595be03ec458c7c68cd19e437c
14e772f6b5bb41f622343296ed3872fc
32edc690019efe46066bc8a22048400e
Sinapova, D (University of Illinois at Chicago)
Monday 24 August 2015,...
Sinapova, D (University of Illinois at Chicago)
Monday 24 August 2015, 11:3012:30
Cambridge University
3780
http://sms.cam.ac.uk/media/2054120
The tree property (session 1)
Sinapova, D (University of Illinois at Chicago)
Monday 24 August 2015, 11:3012:30
The tree propperty at κ says that every tree of height κ and levels of size less than κ has a cofinal branch. A long term project in set theory is to get the consistency of the tree property at every regular cardinal greater than ℵ1. So far we only know that it is possible to have the tree property up to ℵω+1, due to Neeman. The next big hurdle is to obtain it both at ℵω+1 and ℵomega+2 when ℵω is trong limit. Doing so would require violating the singular cardinal hypothesis at ℵomega. In this tutorial we will start with some classic facts about the tree property, focusing on branch lemmas, successors of singulars and Prikry type forcing used to negate SCH. We will then go over recent developments including a dichotomy theorem about which forcing posets are good candidates for getting the tree property at ℵω+1 together with not SCH at ℵω. Finally, we will discuss the problem of obtaining the tree property at the first and double successors of a singular cardinal simultaneously.
20150825T17:55:36+01:00
3780
2054120
true
16x9
false
no

The tree property (session 2)
ucs_sms_2054111_2059202
http://sms.cam.ac.uk/media/2059202
The tree property (session 2)
Sinapova, D (University of Illinois at Chicago)
Tuesday 25 August 2015, 11:3012:30
Tue, 01 Sep 2015 10:42:10 +0100
Isaac Newton Institute
Sinapova, D
826cda4a40274938e0d650781a99eb35
1224b13b20b075bd1f80cd87ae3be8d4
290e03d477552d3d5ee426aa3c36ad93
7c5f13c39bea4982c48a0b2ccf6246f0
Sinapova, D (University of Illinois at Chicago)
Tuesday 25 August 2015,...
Sinapova, D (University of Illinois at Chicago)
Tuesday 25 August 2015, 11:3012:30
Cambridge University
3600
http://sms.cam.ac.uk/media/2059202
The tree property (session 2)
Sinapova, D (University of Illinois at Chicago)
Tuesday 25 August 2015, 11:3012:30
The tree propperty at κ says that every tree of height κ and levels of size less than κ has a cofinal branch. A long term project in set theory is to get the consistency of the tree property at every regular cardinal greater than ℵ1. So far we only know that it is possible to have the tree property up to ℵω+1, due to Neeman. The next big hurdle is to obtain it both at ℵω+1 and ℵomega+2 when ℵω is trong limit. Doing so would require violating the singular cardinal hypothesis at ℵomega. In this tutorial we will start with some classic facts about the tree property, focusing on branch lemmas, successors of singulars and Prikry type forcing used to negate SCH. We will then go over recent developments including a dichotomy theorem about which forcing posets are good candidates for getting the tree property at ℵω+1 together with not SCH at ℵω. Finally, we will discuss the problem of obtaining the tree property at the first and double successors of a singular cardinal simultaneously.
20150901T10:42:10+01:00
3600
2059202
true
16x9
false
no

The tree property (session 3)
ucs_sms_2054111_2059237
http://sms.cam.ac.uk/media/2059237
The tree property (session 3)
Sinapova, D (University of Illinois at Chicago)
Wednesday 26 August 2015, 11:3012:30
Tue, 01 Sep 2015 11:12:22 +0100
Isaac Newton Institute
Sinapova, D
14467fe42b255e39b6db6afd1af90cce
1c162f9166d6c20496f8d16ceed447a3
3238556e48a26eec8ec6680c22f795ca
894c2fc79bb3072a46bba3a400602229
Sinapova, D (University of Illinois at Chicago)
Wednesday 26 August 2015,...
Sinapova, D (University of Illinois at Chicago)
Wednesday 26 August 2015, 11:3012:30
Cambridge University
3548
http://sms.cam.ac.uk/media/2059237
The tree property (session 3)
Sinapova, D (University of Illinois at Chicago)
Wednesday 26 August 2015, 11:3012:30
The tree propperty at κ says that every tree of height κ and levels of size less than κ has a cofinal branch. A long term project in set theory is to get the consistency of the tree property at every regular cardinal greater than ℵ1. So far we only know that it is possible to have the tree property up to ℵω+1, due to Neeman. The next big hurdle is to obtain it both at ℵω+1 and ℵω+2 when ℵω is trong limit. Doing so would require violating the singular cardinal hypothesis at ℵω. In this tutorial we will start with some classic facts about the tree property, focusing on branch lemmas, successors of singulars and Prikry type forcing used to negate SCH. We will then go over recent developments including a dichotomy theorem about which forcing posets are good candidates for getting the tree property at ℵω+1 together with not SCH at ℵω. Finally, we will discuss the problem of obtaining the tree property at the first and double successors of a singular cardinal simultaneously.
20150901T11:12:23+01:00
3548
2059237
true
16x9
false
no

The unreasonable effectiveness of Nonstandard Analysis
ucs_sms_2054111_2141134
http://sms.cam.ac.uk/media/2141134
The unreasonable effectiveness of Nonstandard Analysis
Sanders, S (LudwigMaximiliansUniversität München)
Monday 14th December 2015  15:00 to 15:30
Mon, 21 Dec 2015 16:25:47 +0000
Isaac Newton Institute
Sanders, S
bf8500445910b726d02395ae400d2177
934d991de8ec3d5b4efad6b1c8f8156e
a07f7c62726a5ffbc92da60c76e68a9c
6ac53fe517670d3ec8cdea64182f2b3c
Sanders, S (LudwigMaximiliansUniversität München)
Monday 14th December 2015...
Sanders, S (LudwigMaximiliansUniversität München)
Monday 14th December 2015  15:00 to 15:30
Cambridge University
2380
http://sms.cam.ac.uk/media/2141134
The unreasonable effectiveness of Nonstandard Analysis
Sanders, S (LudwigMaximiliansUniversität München)
Monday 14th December 2015  15:00 to 15:30
The aim of my talk is to highlight a hitherto unknown computational aspect of Nonstandard Analysis. In particular, we provide an algorithm which takes as input the proof of a mathematical theorem from ‘pure’ Nonstandard Analysis, i.e. formulated solely with the nonstandard definitions (of continuity, integration, dif ferentiability, convergence, compactness, et cetera), and outputs a proof of the as sociated effective version of the theorem. Intuitively speaking, the effective version of a mathematical theorem is obtained by replacing all its existential quantifiers by functionals computing (in a specific technical sense) the objects claimed to exist. Our algorithm often produces theorems of Bishop’s Constructive Analysis ([2]). The framework for our algorithm is Nelson’s syntactic approach to Nonstandard Analysis, called internal set theory ([4]), and its fragments based on Goedel’s T as introduced in [1]. Finally, we establish that a theorem of Nonstandard Analysis has the same computational content as its ‘highly constructive’ Herbrandisation. Thus, we establish an ‘algorithmic twoway street’ between socalled hard and soft analysis, i.e. between the worlds of numerical and qualitative results.
References: [1] Benno van den Berg, Eyvind Briseid, and Pavol Safarik, A functional interpretation for non standard arithmetic, Ann. Pure Appl. Logic 163 (2012), no. 12, 1962–1994. [2] Errett Bishop and Douglas S. Bridges, Constructive analysis, Grundlehren der Mathematis chen Wissenschaften, vol. 279, SpringerVerlag, Berlin, 1985. [3] Fernando Ferreira and Jaime Gaspar, Nonstandardness and the bounded functional interpre tation, Ann. Pure Appl. Logic 166 (2015), no. 6, 701–712. [4] Edward Nelson, Internal set theory: a new approach to nonstandard analysis, Bull. Amer. Math. Soc. 83 (1977), no. 6, 1165–1198. [5] Stephen G. Simpson, Subsystems of second order arithmetic, 2nd ed., Perspectives in Logic, CUP, 2009.
20151221T16:25:47+00:00
2380
2141134
true
16x9
false
no

Topological representation of lattice homomorphisms
ucs_sms_2054111_2054134
http://sms.cam.ac.uk/media/2054134
Topological representation of lattice homomorphisms
Blaszczyk, A (University of Silesia in Katowice)
Monday 24 August 2015, 14:0014:30
Tue, 25 Aug 2015 17:39:30 +0100
Isaac Newton Institute
Blaszczyk, A
1294465818ca5a42e69382aba32d7f84
fa5c48c24dba96874104c9e6ea1412f1
3f730d2446ce668390f535f64ad2ef58
83daffb3a6f7fdd624d9fae82edc1d7c
Blaszczyk, A (University of Silesia in Katowice)
Monday 24 August 2015,...
Blaszczyk, A (University of Silesia in Katowice)
Monday 24 August 2015, 14:0014:30
Cambridge University
1818
http://sms.cam.ac.uk/media/2054134
Topological representation of lattice homomorphisms
Blaszczyk, A (University of Silesia in Katowice)
Monday 24 August 2015, 14:0014:30
Wallman proved that if L is a distributive lattice with 0 and 1, then there is a T1space with a base (for closed subsets) being a homomorphic image of L. We show that this theorem can be extended over homomorphisms. More precisely: if Lat denotes the category of normal and distributive lattices with 0 and 1 and homomorphisms, and Comp denotes the category of compact Hausdorff spaces and continuous mappings, then there exists a contravariant functor W:Lat→Comp. When restricted to the subcategory of Boolean lattices this functor coincides with a wellknown Stone functor which realizes the Stone Duality. The functor W carries monomorphisms into surjections. However, it does not carry epimorphisms into injections. The last property makes a difference with the Stone functor. Some applications to topological constructions are given as well.
20150825T17:39:30+01:00
1818
2054134
true
16x9
false
no

Uncountably many maximalclosed subgroups of Sym(N) via reducts of Henson digraphs
ucs_sms_2054111_2090894
http://sms.cam.ac.uk/media/2090894
Uncountably many maximalclosed subgroups of Sym(N) via reducts of Henson digraphs
Agarwal, L (University of Leeds)
Friday 9th October 2015  15:50 to 16:45
Fri, 16 Oct 2015 16:57:28 +0100
Isaac Newton Institute
Agarwal, L
3bbcb6becd8084ec2ce63728e9ee5d72
9d720c178b128cfe678ddc9f77983857
1a920d7004ab65c4765da5e13af7157d
5006bc9159a6e8ff6a169135e84720bd
Agarwal, L (University of Leeds)
Friday 9th October 2015  15:50 to 16:45
Agarwal, L (University of Leeds)
Friday 9th October 2015  15:50 to 16:45
Cambridge University
2788
http://sms.cam.ac.uk/media/2090894
Uncountably many maximalclosed subgroups of Sym(N) via reducts of Henson digraphs
Agarwal, L (University of Leeds)
Friday 9th October 2015  15:50 to 16:45
This work contributes to the two closely related areas of countable homogeneous structures and infinite permutation groups. In the permutation group side, we answered a question of Macpherson that asked to show that there are uncountably many pairwise nonconjugate maximalclosed subgroups of Sym(\mathbb{N}). This was achieved by taking the automorphism groups of uncountably many pairwise nonisomorphic Henson digraphs. The fact these groups are maximalclosed follows from the classification of the reducts of Henson digraphs. In itself, this classification contributes to the building list of structures whose reducts are known and also provides further evidence that Thomas' conjecture is true. In this talk, my main aim will be to describe the construction of these continuum many maximalclosed subgroups, which will include Henson's famous construction of continuum many countable homogeneous digraphs. Any remaining time will be spent giving some of the ideas behind how we prove these groups are maximal closed
20151016T16:57:28+01:00
2788
2090894
true
16x9
false
no

Universal graphs and their variations
ucs_sms_2054111_2103576
http://sms.cam.ac.uk/media/2103576
Universal graphs and their variations
Steprans, J (York University [Canada])
Thursday 22nd October 2015  15:30 to 16:30
Wed, 04 Nov 2015 17:12:59 +0000
Isaac Newton Institute
Steprans, J
d407c434babf974c99a0863bd758a5a5
e6504cc96a9ee3848435a10b82e1959e
6893596148a28fd624a5ad618e2a234c
d0a869ce6236b77db84cdbc10e491047
Steprans, J (York University [Canada])
Thursday 22nd October 2015  15:30 to...
Steprans, J (York University [Canada])
Thursday 22nd October 2015  15:30 to 16:30
Cambridge University
3503
http://sms.cam.ac.uk/media/2103576
Universal graphs and their variations
Steprans, J (York University [Canada])
Thursday 22nd October 2015  15:30 to 16:30
20151104T17:12:59+00:00
3503
2103576
true
16x9
false
no

Universally Baire subsets of 2κ
ucs_sms_2054111_2059244
http://sms.cam.ac.uk/media/2059244
Universally Baire subsets of 2κ
Ikegami, D (Kobe University)
Wednesday 26 August 2015, 13:3014:00
Tue, 01 Sep 2015 09:56:47 +0100
Isaac Newton Institute
Ikegami, D
e2ee5b581b69f656a567acdfe5b2d1d1
529c825c6a2029394d9d1987901033d6
dcfe02d7f6a927e985b5019d10094ffc
9400c6396ea310b6d336ea968ca18d92
Ikegami, D (Kobe University)
Wednesday 26 August 2015, 13:3014:00
Ikegami, D (Kobe University)
Wednesday 26 August 2015, 13:3014:00
Cambridge University
1706
http://sms.cam.ac.uk/media/2059244
Universally Baire subsets of 2κ
Ikegami, D (Kobe University)
Wednesday 26 August 2015, 13:3014:00
In this talk, we present a basic theory of universally Baire subsets of 2κ which generalize that of universally Baire sets of reals due to Feng, Magidor, and Woodin. This is joint work with Matteo Viale.
20150901T09:56:47+01:00
1706
2059244
true
16x9
false
no

Weihrauch degrees of determinacy
ucs_sms_2054111_2141203
http://sms.cam.ac.uk/media/2141203
Weihrauch degrees of determinacy
Pauly, A (University of Cambridge)
Wednesday 16th December 2015  12:00 to 12:30
Mon, 21 Dec 2015 16:47:25 +0000
Isaac Newton Institute
Pauly, A
2a28efe5777195b632839e4b88075fb3
02ad95772916064d4b6ea695098745b7
f8ed1a9c2959bf8f44f885b4781c212f
e8c8745e409ce725c4bbe8abd7c0d028
Pauly, A (University of Cambridge)
Wednesday 16th December 2015  12:00 to...
Pauly, A (University of Cambridge)
Wednesday 16th December 2015  12:00 to 12:30
Cambridge University
1932
http://sms.cam.ac.uk/media/2141203
Weihrauch degrees of determinacy
Pauly, A (University of Cambridge)
Wednesday 16th December 2015  12:00 to 12:30
20151221T16:47:26+00:00
1932
2141203
true
16x9
false
no

Wellquasiorderings for progam analysis and computational complextiy
ucs_sms_2054111_2141189
http://sms.cam.ac.uk/media/2141189
Wellquasiorderings for progam analysis and computational complextiy
Schnoebelen, P [CNRS (Centre national de la recherche scientifique)]
Wednesday 16th December 2015  10:00 to 11:00
Mon, 21 Dec 2015 16:57:53 +0000
Isaac Newton Institute
Schnoebelen, P
8d0a52b9c658b90b7ae92bd936794e0a
76c8c7ffaf454d1e35090efe9df670f0
32a0b257cebfc7dadd98a1c1431935f7
90a74ab516e56a8e64f0f15dcf49cc68
Schnoebelen, P [CNRS (Centre national de la recherche scientifique)]
Wednesday...
Schnoebelen, P [CNRS (Centre national de la recherche scientifique)]
Wednesday 16th December 2015  10:00 to 11:00
Cambridge University
3600
http://sms.cam.ac.uk/media/2141189
Wellquasiorderings for progam analysis and computational complextiy
Schnoebelen, P [CNRS (Centre national de la recherche scientifique)]
Wednesday 16th December 2015  10:00 to 11:00
Coauthor: Sylvain Schmitz (ENS Cachan)
The talk will survey some of the applications of wellquasiorderings in computer science. Wellquasiorderings are an important tool in some areas like program verification, or computeraided deduction and theoremproving. Most importantly, they provide easy proofs for the decidability of logical or combinatorial problems. Recent work by the authors aim at extracting computational complexity bounds from decidability proofs that rely on wellquasiorderings.
20151221T16:57:53+00:00
3600
2141189
true
16x9
false
no

What is a forcing extension (of V)?
ucs_sms_2054111_2059156
http://sms.cam.ac.uk/media/2059156
What is a forcing extension (of V)?
Barton, N (University of London)
Monday 24 August 2015, 13:3014:00
Tue, 01 Sep 2015 09:06:26 +0100
Isaac Newton Institute
Barton, N
bcf4263f743e1406c8238401bdfd036d
d37490294d9887ea43bc1f0c34ecd16c
b32014321c78928a392efe6077a78f64
4efe001659343e487c14412050d90ce0
Barton, N (University of London)
Monday 24 August 2015, 13:3014:00
Barton, N (University of London)
Monday 24 August 2015, 13:3014:00
Cambridge University
1744
http://sms.cam.ac.uk/media/2059156
What is a forcing extension (of V)?
Barton, N (University of London)
Monday 24 August 2015, 13:3014:00
Recent research into the representability of forcing extensions within ground models has often focussed on semantic formulations; we find definable class models within V that express very closely what it means to be a forcing extension of V (such as Hamkins' Naturalist Account of Forcing). In this paper, I argue that while this formulation appears to be a good candidate for interpreting forcing over V, it is problematic in that it is unable to interpret theorems concerning objects below a measurable cardinal whilst keeping the ultrapower wellfounded, and also encounters difficulties in interpreting class forcings. Instead I suggest that the motivation of a strong class theory (such as MK) over V, combined with a syntactic approach to forcing in a strengthened logic, is able to provide an interpretation of various forcing constructions which does not encounter these difficulties.
20150901T09:06:26+01:00
1744
2059156
true
16x9
false
no

Where are the women in medieval logic?
ucs_sms_2054111_2083001
http://sms.cam.ac.uk/media/2083001
Where are the women in medieval logic?
Uckelman, S (Durham University)
Wednesday 2nd September 2015  15:10 to 15:40
Tue, 06 Oct 2015 14:11:45 +0100
Isaac Newton Institute
Uckelman, S
0bba220145a87fb105d750a7d3818559
27c13aaa925b32e88d957825baee9d83
d1e4b295c9cf882c0207cf306ec63549
e17f37b2535d3fffa551ec97e7045584
Uckelman, S (Durham University)
Wednesday 2nd September 2015  15:10 to 15:40
Uckelman, S (Durham University)
Wednesday 2nd September 2015  15:10 to 15:40
Cambridge University
1800
http://sms.cam.ac.uk/media/2083001
Where are the women in medieval logic?
Uckelman, S (Durham University)
Wednesday 2nd September 2015  15:10 to 15:40
20151006T14:11:45+01:00
1800
2083001
true
16x9
false
no
2054111