I am invited to give a talk at the conference Perspectives on Set Theory taking place at IMPAN, Warsaw, Poland on November 13-17, 2023, organized as part of a Simon’s Semester at IMPAN.

The mystery of Woodin limits of Woodin cardinals

Set theory provides a natural framework and powerful tools for calibrating the consistency strength of questions: the large cardinal hierarchy and inner models. The inner model program has been very successful since the 1980’s. However, recent results by Larson, Sargsyan, and Trang show that inner models with a Woodin limit of Woodin cardinals are far out of reach of available methods. The inner model program has reached a turning point. In this talk I will propose two scenarios to attack this barrier: infinite games on natural numbers that last uncountably many steps and supercompact measures on the first uncountable cardinal under determinacy.