Logic Seminar
Gabriel Goldberg
Berkley
The ultrapower axiom: consequences and analogies
Abstract: The ultrapower axiom (UA) is a set theoretic principle abstracted from inner model theory. By design, UA is true in all known canonical inner models of set theory, and it is likely to be true in any model constructed by anything like the current methodology of inner model theory. The consistency of UA with large cardinal axioms at the level of a supercompact therefore provides an important test question and guide in the attempt to generalize inner model theory to this level. In this talk I'll outline the ramifications of UA in large cardinal theory, which turn out to be plentiful, and explain some indirect ways that this theory has helped to answer some questions in set theory unconditionally.
Tuesday February 21, 2023 at 4:00 PM in 636 SEO