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University of Oxford·Sandra Müller
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Determinacy Strength with Universally Baire Sets
Investigating the large cardinal strength of the Axiom of Determinacy under the hypothesis that all sets of reals are universally Baire, proving Sargsyan's conjecture.
Oxford-Bristol Set Theory Seminar Abstract. 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 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.