The announcements are updated continuously. For a list of talks in the coming weeks, please see here.
Hebrew University Set Theory Seminar
Time: Wednesday, 24 April, 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, 24 April, 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
Vienna Research Seminar in Set Theory
Time: Thursday, 25 April, 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
Abstract: Mini-course (25.04.2024 – 16.05.2024, 3 lectures) – 1th 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.
Vienna Logic Colloquium
Time: Thursday, 25 April, 15:00 – 15:50 CEST
Speaker: J. Lopez-Abad, UNED Barcelona
Title: Banach spaces as metric model-theoretical structures
Abstract: Banach spaces are a reach family of metric model structures. We will discuss this in particular focussing on omega-categoricity, ultrahomogeneity and extreme amenability, where also combinatorics plays a crucial role.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
Toronto Set Theory Seminar
Time: Friday, 26 April, 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.
European Set Theory Society 