The announcements are updated continuously. For a list of talks in the coming weeks, please see here.
Hebrew University Set Theory Seminar
Time: Wednesday, 19 June, 13:00-15:00 local time (12:00-14:00 CEST)
Speaker: Yair Hayut
Title: Bristol Like Model over arbitrary model of ZFC (part 2)
Abstract: In this talk I will describe a joint work with Assaf Shani.
In this work we show that for every model of ZFC V there are class many intermediate models of ZF between V and V[c],where c is a Cohen real. Moreover, those models can be symmetric extensions. This illustrates that Usuba’s theorem for limiting the amount of ZFC-grounds under suitable large cardinal axioms cannot limit the amount of ZF-grounds (or intermediate symmetric extensions).
This result extends a result of Asaf Karagila, who constructed the original such intermediate model between V and V[c], in which some combinatorial limitations on the ground model were assumed, limiting the possible large cardinals that are consistent with this scenario.
We will start by presenting some basic features of models of ZF that are measuring how close they are to be models of the axiom of choice (small violation of choice due to Blass and Kinna-Wagner degree). Then, we will give some ideas similar to Monro’s constructions from the 70′ in order to get deeper failures of choice.
We will show how to obtain a model of complete failure of the KW principle using a class forcing and then work in order to obtain some form of a filter for this class forcing using a Cohen real.
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, 20 June, 11:30-13:00 CEST
Speaker: M. Eskew, Unibevrsität Wien
Title: Dense ideals (3/3)
Abstract: This is part of a three talk series. The first installment was on June 6, followed by the presentation on June 13.
In the third and final lecture of this series, we will finish outlining the proof of the consistency result that all ℵn can simultaneously carry dense ideals. This will involve a “uniformization” forcing that follows the Shioya collapse, several strategic closure arguments, and lifting an almost-huge embedding. We will focus on the arguments for getting the result on ℵ1 and ℵ2, and briefly describe how to modify the uniformization forcing to go further.
Information: This talk will be given in hybrid format. Please contact Petra Czarnecki for information how to participate.
European Set Theory Society 