Caltech Logic Seminar Time: Wednesday, 8 September, 12:00 – 1:00pm Pacific time (21:00 CET) Speaker: Zoltán Vidnyánszky, Caltech Title: New examples of bounded degree acyclic graphs with large Borel chromatic number Abstract: Marks proved the existence of dd-regular acyclic Borel graphs with Borel chromatic number d+1. It can be shown that such statements cannot be proved using measures or Baire category, and, indeed, the Borel determinacy theorem had to be invoked. We discuss a generalization of Marks’ method, which leads to an interesting new class of examples of 3-regular acyclic Borel graphs, which we call homomorphism graphs. This yields new proofs of a number of known results. As a new application, we show that it is hard to decide whether the Borel chromatic number of a Borel graph is ≤3, even for acyclic 3-regular graphs (that is, such graphs form a Σ21-complete set). Joint work with Jan Grebík. Information: Please see the seminar webpage.
Helsinki Logic Seminar Time: Wednesday, 8 September, 12:00 – 14:00 Helsinki time (11:00-13:00 CET) Speaker: Mark Kamsma Title: Independence Relations in Abstract Elementary Categories Abstract: In Shelah’s stability hierarchy we classify theories using combinatorial properties. Some important classes are: stable, simple and NSOP1 each being contained in the next. We can characterise these classes by the existence of a certain independence relation. For example, in vector spaces such an independence relation comes from linear independence. Part of this characterisation is canonicity of the independence relation: there can be at most one nice enough independence relation in a theory. Lieberman, Rosický and Vasey proved canonicity of stable-like independence relations in accessible categories. Accessible categories are a very general framework. The category of models of some theory is an accessible category, every AEC (abstract elementary class) is an accessible category, but even then accessible categories are more general. Inspired by this we introduce the framework of AECats (abstract elementary categories) and prove canonicity for simple-like and NSOP1-like independence relations. This way we reconstruct part of the hierarchy that we have for first-order theories, but now in the very general category-theoretic setting. Information: Please see the seminar webpage.
CMU Model Theory Seminar Time: Thursday, 9 September, 11:00 Eastern Daylight Time (17:00 CET) Speaker: Will Boney, Texas State University Title: Model Theoretic Characterizations of Large Cardinals, Part I Abstract: Large cardinals in set theory are typically characterized in a variety of ways. This talk focuses on characterizing large cardinals through model-theoretic compactness principles. Inspired by the work of Benda, we begin by showing that normality of ultrafilters corresponds to type omission. We will then move onto stronger logics and more exotic cardinals, including using Woodin cardinals to motivate an abstract definition of Henkin structures. Some of this work is joint with Dimopoulos, Gitman, and Magidor. Information: Please see the seminar webpage
Here’s a popular science interview of Joel David Hamkins by mathematician Daniel Rubin on his show from 26 August 2021, with a lively, wideranging discussion spanning mathematics, infinity, and the philosophy of mathematics. Please enjoy!
Caltech Logic Seminar Time: Monday, 30 August, 12:00 – 1:00pm Pacific time (21:00 CET) Speaker: Gábor Kun, Alfréd Rényi Institute of Mathematics Title: Measurable perfect matchings Abstract: We go through the history of measurable perfect matchings from the Banach-Tarski paradox via circle squaring and report on recent progress. We construct a dd-regular treeing (for every d>2d>2) without a measurable perfect matching. We show that the Hall condition is essentially sufficient in the hyperfinite, one-ended, bipartite case. This allows us to characterize bipartite Cayley graphs with factor of i.i.d. perfect matchings extending the Lyons-Nazarov theorem. We apply these to Gardner’s conjecture for uniformly distributed sets, to balanced orientations, and to get new, simple proofs of the measurable circle squaring. We prove the analogous theorems in the context of rounding flows, too. Partially joint work with Matt Bowen and Marcin Sabok. Information: Check on the seminar webpage if the seminar will take place.
Logic Seminar, Carnegie Mellon University Time: Tuesday, 31 August, 3:30 – 4:30pm Eastern Standard Time (21:30 – 22:30 CET) Speaker: Felix Weilacher, Carnegie Mellon University Title: Borel Edge Colorings for Finite Dimensional Groups Abstract: In Borel graph combinatorics, one often produces a structure (e.g. a coloring) by dividing a graph into subgraphs with finite connected components, then defining the structure on those components via some straightforward uniformization result. We first give an overview of some recent work formalizing these notions and applying them to various problems. We then present our own application to the problem of edge coloring. For Borel actions of certain groups, we find “degree plus one” Borel edge colorings, matching the classical bound of Vizing. Furthermore, for finitely generated abelian groups, we are able to exactly determine Borel edge chromatic numbers. Information: Zoom link https://cmu.zoom.us/j/621951121, meeting ID: 621 951 121
RIMS workshop “Recent Developments in Set Theory of the Reals
Date: Tuesday, October 12, 2021 to Friday, October 15, 2021 Venue: ONLINE (via ZOOM meeting), based on Japan Standard Time 9am–5pm Contact: Masaru Kada (Osaka Prefecture University) / firstname.lastname@example.org
Workshop Overview: This online workshop, hosted by RIMS (Research Institute for Mathematical Sciences, Kyoto University), is mainly (but not only) focused on recent developments in set theory of the reals. The program will contain a minicourse (a series of lectures) as well as contributed talks. In the minicourse, we invite Joerg Brendle (Kobe University) and Diego Mejia (Shizuoka University), who will give us lectures on some forcing techniques (e.g., Boolean ultrapowers, submodel methods, etc.) and related results in set theory of the reals.We welcome every researcher in set theory or related research fields. Please join us!
Online Logic Seminar Time: Thursday, 26 August, 01:00pm US central time (20:00 CET) Speaker: Colin Jahel, Université Claude Bernard Lyon 1 Title: Some progress on the unique ergodicity problem Abstract: In 2005, Kechris, Pestov and Todorcevic exhibited a correspondence between combinatorial properties of structures and dynamical properties of their automorphism groups. In 2012, Angel, Kechris and Lyons used this correspondence to show the unique ergodicity of all the minimal actions of some subgroups of S∞. In this talk, I will give an overview of the aforementioned results and discuss recent work generalizing results of Angel, Kechris and Lyons in several directions. Information: See the seminar webpage.
Singapore Logic Seminar Time: Wednesday, 18 August, 16:00-17:00 Singapore time (10:00-11:00 CET) Speaker: Yu Liang Title: Generalizing Besicovitch-Davis theorem Abstract: Besicovitch-Davis theorem says that the Hausdorff dimension of every analytic set can be approximated by its closed subset. But the Besicovitch-Davis theorem fails for co-analytic sets under the assumption V=L as observed by Slaman. We prove that the theorem holds for arbitrary sets under ZF+sTD. We also prove that the theorem holds for Σ12-sets under Martin’s axiom. This is joint work with Peng Yinhe and Wu Liuzhen. Information: See the seminar webpage.
Logic Seminar, Carnegie Mellon University Time: Tuesday, 10 August, 3:30 – 4:30pm Eastern Standard Time (21:30 – 22:30 CET) Speaker: Nathaniel Bannister, Carnegie Mellon University Title: Additivity of strong homology for locally compact separable metric spaces, part 6 Abstract: This series of talks will cover the 2019 paper “On the additivity of strong homology for locally compact separable metric spaces” as well as recent work establishing a conceptual basis for the results therein. We will show that (relative to a weakly compact cardinal) it is consistent for strong homology to be additive and compactly supported on the class of locally compact separable metric spaces. In the process, we develop an equivalent algebraic statement and a sufficient cardinal-theoretic condition. This is joint work with Justin Moore, Jeffrey Bergfalk, and Stevo Todorcevic. Information: Zoom link https://cmu.zoom.us/j/621951121, meeting ID: 621 951 121
apore Logic Seminar Time: Wednesday, 11 August, 16:00-17:00 Singapore time (10:00-11:00 CET) Speaker: Frank Stephan, National University of Singapore Title: A survey on the structures realised by positive equivalence relations Abstract: Let a positive equivalence relation to be an r.e. equivalence relation on the set of natural numbers with infinitely many equivalence relations. Khoussainov initiated with coauthors a deep study of the following question: Given a positive equivalence relation eta, which structures from a given set of structures does this equivalence relation realise? Here realisation means that functions in the structure are recursive and relations are r.e. with the equality itself given by the equivalence relation eta. In other words, the given r.e. structure divided by eta is the structure realised by eta. Now questions studied by Khoussainov and his coworkers included questions like “What is the partial ordering on positive equivalence relations eta,rho where eta is below rho iff every structure of the given type realised by eta is also realised by rho? Besides algebraic structures and orders, it has also been studied how the learnability notions behave with respect to uniformly r.e. one-one families realised by positive equivalence relations. Information: See the seminar webpage.
CUNY Set Theory Seminar Time: Friday, 13 August, 2pm New York time (20:00 CET) Speaker: Adrian Mathias, University of Freiburg Title: Linking descriptive set theory to symbolic dynamics: Part II Abstract: 1. I’ll begin by reviewing the work I did in 1993-6 on a problem raised by the dynamics group at the Universidad Autonomoa de Barcelona. They were interested in a phenomenon that resembles the Cantor-Bendixson sequence of derivatives, and hoped to prove that the sequence would always stop at a countable stage. Using ideas of Kunen and Martin I showed that it would always stop at or before stage omega_1. 2. In 2002/3, alerted by observations of David Fremlin, to the possibility that the barcelona conjecture was false, I succeeded in constructing an example with recursive initial data where the sequence stops exactly at stage omega_1. My Réunion colleague Christian Delhommé simplified and extended my ideas. I’ll outline the construction, as I think the underlying idea might have applications elsewhere in descriptive set theory. 3. I will outline more recent work using ideas of Blass and Fremlin to to study ‘uniform’ versions of the results of 1993-96. I’ll end with listing some open problems which I hope will be found interesting. Information: The seminar will take place virtually. Please email Victoria Gitman (email@example.com) for the meeting id.
Logic Seminar, Carnegie Mellon University Time: Tuesday, 27 July, 3:30 – 4:30pm Eastern Standard Time (21:30 – 22:30 CET) Speaker: Nathaniel Bannister, Carnegie Mellon University Title: Additivity of strong homology for locally compact separable metric spaces, part 3 Abstract: This series of talks will cover the 2019 paper “On the additivity of strong homology for locally compact separable metric spaces” as well as recent work establishing a conceptual basis for the results therein. We will show that (relative to a weakly compact cardinal) it is consistent for strong homology to be additive and compactly supported on the class of locally compact separable metric spaces. In the process, we develop an equivalent algebraic statement and a sufficient cardinal-theoretic condition. This is joint work with Justin Moore, Jeffrey Bergfalk, and Stevo Todorcevic. Information: Zoom link https://cmu.zoom.us/j/621951121, meeting ID: 621 951 121
Hebrew University-Bar Ilan University Set Theory seminar Time: Wednesday, 28 July 14:00-16:00 Israel Time (13:00-15:00 CET) Speaker: tba Title: tba Abstract: tba Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.
Toronto Set Theory Seminar Time: Friday, 30 July, 1.30-3pm Toronto time (19:30-21:00 CET) Speaker: tba Title: tba Abstract: tba Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.
CUNY Set Theory Seminar Time: Friday, 30 July, 2pm New York time (20:00 CET) Speaker: Neil Barton, University of Konstanz Title: Countabilism and Maximality (or ‘Some Systems of Set Theory on which Every Set Is Countable’) Abstract: It is standard in set theory to assume that Cantor’s Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor’s Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that the continuum is a proper class. We examine several theories based on maximality considerations in this framework (in particular countabilist analogues of reflection principles) and show how standard set theories (including ZFC with large cardinals added) can be incorporated. We conclude that the systems considered raise questions concerning the foundational purposes of set theory. Information: The seminar will take place virtually. Please email Victoria Gitman (firstname.lastname@example.org) for the meeting id.