Tom Benhamou : Saturation properties of ultrafilters

Posted by Tom Benhamou , part of the Logic Seminar.

At

Feb. 7, 2023, 4 p.m.

In

636 SEO

Abstract

In this talk, we will focus on certain saturation properties of filters and ultrafilters which generalizes the so-called Galvin property. In the first part of the talk, we will present a connection between such ultrafilters and the existence of Slim-Kurepa trees. We will then present several results regarding the existence of non-Galvin ultrafilters under several large cardinal assumptions. Finally, if time permits, we will present a recent application to canonical inner models and some open related questions.