Kurt Gödel Research Center

2015 seminar talk: The inner model problem and descriptive inner model theory

Talk held by Rachid Atmai (KGRC) at the KGRC seminar on 2015-10-08.

Abstract

We will introduce one of the main problems in inner model theory (IMT). A solution to this problem is crucial for inner models of large cardinals to be canonical (in particular for their set of reals to be definable). Descriptive set theory (DST) meets IMT at multiple levels: first at the structural level of correspondence between inner models with Woodin cardinals and determinacy axioms then in the HOD analysis and the core model induction for example; second, it appears that DST is absolutely necessary to make progress on the inner model problem through the study of the universally Baire sets of reals and the strong determinacy models these sets live in. The goal of the talk is to introduce these notions and the ideas at play in this field.