I was invited to give an invited address at the 2023 Winter Meeting of the Association for Symbolic Logic with the JMM in Boston, USA, January 4-7, 2023.

Universally Baire Sets, Determinacy, and Inner Models

Computing the large cardinal strength of a given statement is one of the key research directions in set theory. Fruitful tools to tackle such questions are given by inner model theory. The study of inner models was initiated by Gödel’s analysis of the constructible universe $L$. Later, it was extended to canonical inner models with large cardinals, e.g., measurable cardinals, strong cardinals or Woodin cardinals, which were introduced and studied by Jensen, Mitchell, Steel, Woodin, Sargsyan, and others. We will outline the role universally Baire sets play in the study of inner models and their connections to determinacy axioms. In particular, we will discuss recent results on $\mathsf{Sealing}$, a formalization due to Woodin of the statement that the theory of the universally Baire sets cannot be changed by forcing.