I was invited to give a talk in the special session on set theory at the Logic Colloquium 2022 that took place in Reykjavik, Iceland, June 27 - July 1, 2022.

A stationary-tower-free proof of $\mathsf{Sealing}$ from a supercompact

$\mathsf{Sealing}$ is a generic absoluteness principle for the theory of the universally Baire sets of reals introduced by Woodin. It is deeply connected to the Inner Model Program and plays a prominent role in recent advances in inner model theory. Woodin showed in his famous Sealing Theorem that in the presence of a proper class of Woodin cardinals $\mathsf{Sealing}$ holds after collapsing a supercompact cardinal. I will outline the importance of $\mathsf{Sealing}$ and discuss a new and stationary-tower-free proof of Woodin’s Sealing Theorem that is based on Sargsyan’s and Trang’s proof of $\mathsf{Sealing}$ from iterability. This is joint work with Grigor Sargsyan and Bartosz Wcisło.