I am invited to give an invited talk at the British Logic Colloquium in Bristol, UK, September 7 - 8, 2023.
Generic absoluteness for the definable powerset of the universally Baire sets
Universally Baire sets play an important role in studying canonical models with large cardinals. But to reach higher large cardinals more complicated objects, for example, canonical subsets of universally Baire sets come into play. Inspired by inner model theory, we introduce the definable powerset of the universally Baire sets and show that, after collapsing a large cardinal, the constructible universe of the definable powerset of the universally Baire sets is a model of determinacy and its theory cannot be changed by forcing. Even though the work is inspired by inner model theory, the techniques do not use any fine structure. This is joint work with Grigor Sargsyan. The talk will be introductory and all relevant concepts and ideas will be introduced.