The consistency strength of determinacy when all sets are universally Baire

Abstract

It is known that the large cardinal strength of the Axiom of Determinacy when enhanced with the hypothesis that all sets of reals are universally Baire is much stronger than the Axiom of Determinacy itself. Sargsyan conjectured it to be as strong as the existence of a cardinal that is both a limit of Woodin cardinals and a limit of strong cardinals. Larson, Sargsyan and Wilson used a generalization of Woodin's derived model construction to show that this conjectured result would be optimal. In this paper we introduce a new translation procedure for hybrid mice extending work of Steel, Zhu and Sargsyan and apply it to prove Sargsyan's conjecture.