Forum of Mathematics, Sigma (Jan 2024)
The exact consistency strength of the generic absoluteness for the universally Baire sets
Abstract
A set of reals is universally Baire if all of its continuous preimages in topological spaces have the Baire property. $\mathsf {Sealing}$ is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that the theory of the universally Baire sets cannot be changed by forcing.