The consistency strength of determinacy when all sets are universally Baire

TL;DR

This paper proves Sargsyan's conjecture that the large cardinal strength of determinacy with all sets universally Baire matches a specific strong large cardinal hypothesis, using a new translation procedure for hybrid mice.

Contribution

Introduces a novel translation method for hybrid mice and applies it to confirm the conjectured strength of determinacy with universally Baire sets.

Findings

Confirmed Sargsyan's conjecture on the strength of determinacy with universally Baire sets.

Developed a new translation procedure for hybrid mice extending previous work.

Established the optimality of the large cardinal strength associated with this form of determinacy.

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.