Berkeley Conference in Inner Model Theory

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

The Berkeley Conference on Inner Model Theory will be held July 8-19, 2019 at the Department of Mathematics, University of California, Berkeley. It will be devoted to significant recent progress in inner model theory. The new work includes advances in iteration tree combinatorics, leading to a general comparison theorem for the iteration strategies of mice having no long extenders, and from there to a new theory of the hereditarily ordinal definable sets in models of the Axiom of Determinacy. The Berkeley conference will gather experts in inner model theory from around the world, as well as students and postdocs with a serious interest in the field, in order to communicate and pursue the new ideas. Large cardinal hypotheses play a central role in the set-theoretic foundations of mathematics. The inner model program attempts to associate to each large cardinal hypothesis a canonical minimal universe of sets in which that hypothesis is true. Some of our deepest understanding of large cardinal hypotheses come from this program. The core model induction method is our most powerful method for constructing such canonical inner models, and this conference will be devoted to recent work that strengthens the method in important ways. The website for the conference is https://ivv5hpp.uni-muenster.de/u/rds/berkeley_meeting_2019.html. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.