### Philosophical implications of some recent breakthroughs in set theory

#### Speaker:

Joan Bagaria  (University of Barcelona)

We shall discuss the foundational and philosophical implications of some recent results in set theory, such as Woodin’s HOD-Dichotomy theorem, the proof by Aspero-Schindler that MM++ implies the (*) axiom, and some theorems, due to several authors, that provide new in- sights into the hierarchy of large cardinals, including large cardinals that contradict the Axiom of Choice.