I am invited to give a talk in the Logic Colloquium of the University of Vienna on March 19, 2026.

Sealing the universe: How far can inner model theory reach?

The inner model program is one of the central pillars of modern research in set theory. Grounded in Gödel’s work, it aims at reaching stronger and stronger canonical inner models for large cardinals. These inner models provide a controlled environment to study the structural behaviour of large cardinals and can be regarded as witnesses for their consistency. But the program is currently undergoing a revolution: Established methods such as Woodin’s Core Model Induction provably fail even below a Woodin limit of Woodin cardinals. This is grounded in a principle called Sealing. In this talk we will outline the impact Sealing has on the inner model program as well as scenarios for overcoming the obstacles introduced by Sealing for a non-expert audience.