# Algebra Seminar talk

2023-05-12

Takehiko **Gappo***Chang-type models of determinacy*

Abstract:

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.