The announcements are updated continuously. For a list of talks in the coming weeks, please see here.
CMU Core Model Seminar
Time: Tuesday, 19 March, 1:30 – 3:00pm Pittsburgh time (18:30 – 20:00 CET)
Speaker: Nam Trang, University of North Texas
Title: Ideals and Strong Axioms of Determinacy (part 2)
Abstract: We present the main ideas behind the proof of the equiconsistency of the theories:
(1) ZF + AD_R + \Theta is regular.
(2) ZFC + CH + there is an \omega_1-dense ideal on \omega_1.
(3) ZFC + the nonstationary ideal on P_{\omega_1}(R) is strong and pseudo-homogeneous.
This resolves a long-standing open problem asked by W.H. Woodin in the 1990’s. In the first talk, we discuss some history related to this problem and the general program in descriptive inner model theory that aims to calibrate the consistency strength of theories like the above. In the next two talks, we outline some main ideas behind the proof: the forcing construction that shows (1) is an upper bound (consistency-wise) of (2) and (3), and the core model induction that shows (2), (3) are upper bounds for (1).
Information: Please email ernest Schimmerling in advance for the login.
CMU Logic Seminar
Time: Tuesday, 19 March, 3:30 – 4:30pm Pittsburgh time (20:30 – 21:30 CET)
Speaker: Denis Hirschfeldt, University of Chicago
Title: Reductions between problems in reverse mathematics and computability theory
Abstract: Many mathematical principles can be stated in the form “for all X such that C(X) holds, there is a Y such that D(X,Y) holds”, where X and Y range over second-order objects, and C and D are arithmetic conditions. We can think of such a principle as a problem, where an instance of the problem is an X such that C(X) holds, and a solution to this instance is a Y such that D(X,Y) holds. I will discuss notions of reducibility between such problems coming from the closely-related perspectives of reverse mathematics and computability theory.
Information: See the seminar webpage.
Hebrew University Set Theory Seminar
Time: Wednesday, 20 March, 13:00-15:00 local time (12:00-14:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: This talk will be given in hybrid format. Please contact Omer Ben-Neria for information how to participate.
Vienna Research Seminar in Set Theory
Time: Thursday, 21 March, 11:30-13:00 CET
Speaker: Martina Iannella, TU Wien
Title: (Piecewise) convex embeddability on linear orders
Abstract: Given a nonempty set L of linear orders, we say that the linear order L is L-convex embeddable into the linear order L′ if it is possible to partition L into convex sets, indexed by some element of L, which are isomorphic to convex subsets of L′ ordered in the same way. This notion generalizes convex embeddability and (finite) piecewise convex embeddability, which arise from the special cases L={1} and L=Fin. In this talk we focus on the behaviour of these relations on the set of countable linear orders, first characterising when they are transitive, and hence a quasi-order. We then look at some combinatorial properties and complexity (with respect to Borel reducibility) of these quasi-orders. Finally, we analyse their extension to uncountable linear orders.
The presented results stem from joint work with Alberto Marcone, Luca Motto Ros, and Vadim Weinstein.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
Vienna Logic Colloquium
Time: Thursday, 21 March, 15:00 – 15:50 CET
Speaker: K. Krupiński, University of Wrocław
Title: On some applications of model theory and topological dynamics to additive combinatorics
Abstract: Model theory is a fast growing branch of mathematical logic with deep interactions with algebra, algebraic geometry, combinatorics, and, more recently, topological dynamics. I will focus on a few interactions with topological dynamics, and applications to additive combinatorics.
I will discus type-definable components of definable groups, which lead to model-theoretic descriptions of Bohr compactificatios of groups and rings, and also to so-called locally compact models of approximate subgroups and subrings which in turn are crucial to get structural or even classification results about approximate subgroups and subrings. I will discuss my result that each approximate subring has a locally compact model, and mention some structural applications. In contrast to approximate subrings, not every approximate subgroup has a locally compact model. However, Ehud Hrushovski showed that instead it has such a model in a certain generalized sense (with morphisms replaced by quasi-homomorphisms). In order to do that, he introduced and developed local logics and definability patterns. In my recent paper with Anand Pillay, we gave a shorter and simpler construction of a generalized locally compact model, based on topological dynamics methods in a model-theoretic context. I will briefly discuss it, if time permits.
Information: This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.
New York Set Theory Seminar
Time: Friday, 22 March, 12.30-1.45pm New York time (17.30-19.45 CET)
Speaker: Arthur Apter, CUNY
Title: A choiceless answer to a question of Woodin
Abstract: In a lecture presented in July 2023, Moti Gitik discussed the following question from the 1980s due to Woodin, as well as approaches to its solution and why it is so difficult to solve: Question: Assuming there is no inner model of ZFC with a strong cardinal, is it possible to have a model M of ZFC such that M⊨’2ℵω>ℵω+2 and 2ℵn=ℵn+1 for every n<ω’, together with the existence of an inner model N∗⊆M of ZFC such that for the γ,δ so that γ=(ℵω)M and δ=(ℵω+3)M, N∗⊨’γ is measurable and 2γ≥δ’?
I will discuss how to find answers to this question, if we drop the requirement that M satisfies the Axiom of Choice. I will also briefly discuss the phenomenon that on occasion, when the Axiom of Choice is removed from consideration, a technically challenging question or problem becomes more tractable. One may, however, end up with models satisfying conclusions that are impossible in ZFC.
Reference: A. Apter, ‘A Note on a Question of Woodin’, Bulletin of the Polish Academy of Sciences (Mathematics), volume 71(2), 2023, 115–121.
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 22 March, 1.30-3.00pm Toronto time (18.30-20.00 CET)
Speaker: Frank Tall, University of Toronto
Title: Grothendieck spaces
Abstract: In 1952 Grothendieck proved a result connecting the question of when countably compact subspaces of certain function spaces are compact with the ability to interchange double limits, as is often done in Analysis. Iovino and colleagues connected the interchange of double limits to questions of definability of pathological Banach spaces. In his recent lecture in this seminar, he connected that interchange to questions in Machine Learning. With my recent Ph.D. student, Clovis Hamel, I extended Iovino’s work to deal with such definability in not necessarily compact logics. Previously I had answered questions of Arhangel’skii concerning generalizations of Grothendieck’s work by showing they were undecidable. Today I will speak about the topology involved in both of these endeavours.
Information: Please see the conference webpage for the login information.
European Set Theory Society 