I am invited to give a talk in the Logic Seminar at CMU on April 20th, 2021 at 3:30pm Pittsburgh time (which is 9:30pm Vienna time). This one hour talk will be for a general audience. Afterwards I will give a 90min talk in the reading group where I will give more technical details. This seminar will take place virtually via zoom.
Large cardinals and determinacy when 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 that this would be optimal via a generalization of Woodin’s derived model construction. After a gentle introduction to the connection between determinacy axioms and large cardinals we will sketch a proof of Sargsyan’s conjecture.
The exact consistency strength of “AD + all sets are universally Baire”
In this second talk, we will outline the proof of Sargsyan’s conjecture with more details. In particular, we will discuss a new translation procedure for hybrid mice extending work of Steel, Zhu and Sargsyan that is crucial in the construction of a model with a cardinal that is both a limit of Woodin cardinals and a limit of strong cardinals from a model of the Axiom of Determinacy in which all sets of reals are universally Baire.