The announcements are updated continuously. For a list of talks in the coming weeks, please see here.
Hebrew University Set Theory Seminar
Time: Wednesday, 1 May, 13:00-15:00 local time (12:00-14:00 CEST)
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.
Leeds Models and Sets Seminar
Time: Wednesday, 1 May, 14:00-15:00 local time (15:00-16:00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Zoom link: https://universityofleeds.zoom.us/j/89414887798?pwd=SmRXMGwvUWkvYWptVUlnZHZpeFF5UT09
Caltech Logic Seminar
Time: Wednesday, 1 May, 12:00 – 13:00pm Pacific time (21:00 – 22:00 CEST)
Speaker: Robert Simon, London School of Economics and Political Science
Title: Paradoxical decompositions and colouring rules
Abstract: A colouring rule is a way to colour the points x of a probability space according to the colours of finitely many measures preserving tranformations of x. The rule is paradoxical if the rule can be satisfied a.e. by some colourings, but by none whose inverse images are measurable with respect to any finitely additive extension for which the transformations remain measure preserving. We demonstrate paradoxical colouring rules defined via u.s.c. convex valued correspondences (if the colours b𝑏 and c𝑐 are acceptable by the rule than so are all convex combinations of b𝑏 and c𝑐). This connects measure theoretic paradoxes to problems of optimization and shows that there is a continuous mapping from bounded group-invariant measurable functions to itself that doesn’t have a fixed point (but does has a fixed point in non-measurable functions).
Information: See the seminar webpage.
Vienna Research Seminar in Set Theory
Time: Thursday, 2 May, 11:30-13:00 CEST
Speaker: C. B. Switzer, Universität Wien
Title: Baumgartner’s Axiom and Cardinal Characteristics: A Sparse Look at Dense Sets of Reals II
Abstract: Mini-course (25.04.2024 – 16.05.2024, 3 lectures) – 2nd lecture:
Given a cardinal κ, a set of reals A⊆R is κ-dense if its intersection with any open interval has size κ. Baumgartner’s axiom (BA) — proved consistent by Baumgartner in 1973 — states that all ℵ1-dense sets of reals are order isomorphic with the induced linear order from R. This is the most straightforward generalization to the uncountable of Cantor’s proof that all countable dense linear orders without endpoints are order isomorphic. BA has variations to other topological spaces — given a topological space X, a subset A⊆X is κ-dense if its intersection with each non-empty open subset has size κ. The axiom BA(X) states that given any two ℵ1-dense subsets of X, say A and B, there is an autohomeomorphism of X mapping A onto B. In this parlance BA is equivalent to BA(R). Surprisingly BA is not equivalent to BA(Rn) for any finite 1<n<ω. In fact BA does not follow from Martin’s Axiom (Abraham-Rubin-Shelah) though BA(Rn) does (in fact from p>ℵ1) for each n>1 (Steprāns-Watson).
In these three lectures I will discuss these ideas and some related ones including the question of when BA(X) implies BA(Y) for Polish spaces X and Y. Central to these questions are the role of cardinal characteristics including the celebrated theorem of Todorčević that BA implies b>ℵ1 as well as a recent, higher dimensional analogue of this result that for any n<ω BA(Rn) implies b>ℵ1 (S.-Steprāns). There are many beautiful open problems in this area and I plan to make discussing them a focal point of the talks. The talks will start slowly and should be accessible to students. Time permitting, the final talk will include some new results. If and when these results are presented, they are joint work with Juris Steprāns.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Cross-Alps Logic Seminar
Time: Friday, 3 May, 16.00-17.00 CEST
Speaker: S. Unger, University of Toronto
Title: Iterated ultrapower methods
Abstract: We develop some of the basic theory of iterated ultrapowers and survey some old and new results in singular cardinal combinatorics whose proofs can be phrased in terms of them.
Information: The event will stream on the Webex platform. Please write to luca.mottoros [at] unito.it for the link to the event.
New York Set Theory Seminar
Time: Friday, 3 May, 12.30-1.45pm New York time (18.30-20.45 CEST)
Speaker: Spencer Unger, University of Toronto
Title: Iterated ultrapower methods in analysis of Prikry type forcing
Abstract: We survey some old and new results in singular cardinal combinatorics whose proofs can be phrased in terms of iterated ultrapowers and ask a few questions.
Information: Please see the conference webpage for the login information.
Toronto Set Theory Seminar
Time: Friday, 3 May, 1.30-3.00pm Toronto time (19.30-21.00 CEST)
Speaker: tba
Title: tba
Abstract: tba
Information: Please see the conference webpage for the login information.