I was invited to give a talk on June 6, 2025, as well as a tutorial from June 30 to July 3,2025 at the Berkeley Inner Model Theory Conference.

Talk: Translating between large cardinals and iteration strategies

My PhD thesis under Ralf’s supervision focused on mice with finitely many Woodin cardinals, the projective complexity of their iteration strategies and models of levels of projective determinacy. Since then, I have been interested to connect inner models with large cardinals and models of determinacy at various levels. In this talk I will outline some classical results as well as new developments in this area.

Tutorial. Derived models from genericity iterations

Woodin’s derived model theorem as well as Steel’s stationary-tower-free proof of it are powerful tools to construct models of determinacy. We outline Steel’s proof of the stationary-tower-free version using genericity iterations as well as iterability. Moreover, we sketch recent extensions to models of determinacy with non-trivial sets of sets of reals, obtained jointly with Sargsyan, as well as applications of this method, obtained jointly with Koschat and Sargsyan.

Lecture notes are available on the conference website.