Algebra Seminar talk

Takehiko Gappo
Chang-type models of determinacy

A few years ago, a new model of the Axiom of Determinacy was introduced by Grigor Sargsyan. The model is ``Chang-type, in the sense that it contains $\delta^{\omega}$ for some ordinal $\delta>\Theta$. First we will present two recent results using such a Chang-type model of determinacy. One is the proof of determinacy in the Chang model from a hod mouse with a Woodin limit of Woodin cardinals, and the other is a consistency result on omega-strongly measurable cardinals in HOD. Then we will also talk about the construction of a Chang-type model of determinacy with supercompact measures, which extends the aforementioned result of Sargsyan.

This talk is based on several joint works with Navin Aksornthong, James Holland, Sandra Müller, and Grigor Sargsyan.