I will give a talk in the KGRC Research Seminar at University of Vienna on Mar 11th, 2021 at 3pm Vienna time. The seminar will take place via zoom.
The exact consistency strength of “$AD^+$ + all sets are universally Baire”
The large cardinal strength of the Axiom of Determinacy when enhanced with the hypothesis that all sets of reals are universally Baire is known to be much stronger than the Axiom of Determinacy itself. In fact, 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 showed in 2014 that this would be optimal via a generalization of Woodin’s derived model construction. We will discuss a new translation procedure for hybrid mice extending work of Steel, Zhu and Sargsyan and use this to prove Sargsyan’s conjecture.