I was invited to give an invited talk at the first Gdansk Logic Conference, University of Gdansk, Poland, May 5-7, 2023.
Determinacy and generic absoluteness for the definable powerset of the universally Baire sets
Inspired by core model induction, we introduce the definable powerset A∞ of the universally Baire sets Γ∞ and show that, after collapsing a large cardinal, L(A∞) is a model of determinacy and its theory cannot be changed by forcing. Our main technical tool is an iteration that realizes the universally Baire sets as the sets of reals in a derived model of some iterate of V, from a supercompact cardinal κ and a proper class of Woodin cardinals. This is joint work with Grigor Sargsyan.