

Generic absoluteness for the definable powerset of the universally Baire sets
By Sandra Müller
Appears in collection : XVII International Luminy Workshop in Set Theory / XVII Atelier International de Théorie des Ensembles
We show that starting from an inaccessible limit of supercompact cardinals, there is a staionary set preserving forcing so that the Nonstationary Ideal is dense in the generic extension. This answers positively a question of Woodin.