Forum of Mathematics, Sigma (Jan 2024)

The exact consistency strength of the generic absoluteness for the universally Baire sets

  • Grigor Sargsyan,
  • Nam Trang

DOI
https://doi.org/10.1017/fms.2023.127
Journal volume & issue
Vol. 12

Abstract

Read online

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.