Event Detail

The Inner Model Program, which is a key component of Gödel’s Program, aims to build canonical inner models for large cardinal axioms. The least canonical inner model is Gödel’s constructible universe L, and one of the desired features of these inner models is L-likeness. Unlike the cumulative hierarchy, the L-hierarchy evolves by restricting only to definable sets, which leads to a very restricted notion of the powerset operation. This has led to a commonly held belief that the powerset operation inside inner models is simple, and therefore, the universe of sets cannot be an inner model—otherwise, everything would be very simple. In fact, we will show that, surprisingly, the most robust generically absolute notion of definability—universally Baire definability—is not powerful enough to capture the powerset operation in very small inner models. We will then explore generically absolute notions of definability discovered in recent years that go beyond universally Baire sets. The series of talks will conclude with a view of the universe of sets based on Nairian Models. All three talks will be aimed at a general audience.