Departmental Colloquium
Gabriel Goldberg
UC Berkeley
The Large Cardinal Program
Abstract: One of the main goals of logic is to classify mathematical theories according to their strength. Since Cohen's 1964 proof of the independence of the continuum hypothesis, set theorists have discovered a staggering array of mutually incompatible set theories, and so such a classification may initially seem impossible. But in fact, it seems that each of these theories corresponds to a level of a single linear hierarchy of theories: the large cardinal hierarchy. These are the theories formed from the standard ZFC axioms by adding generalizations of the axiom of infinity, or large cardinal axioms. Whether this correspondence extends to the strongest known theories is open, and this talk will discuss how this question is related to canonical models of set theory and large cardinal axioms so strong they are inconsistent with the axiom of choice.
Monday February 20, 2023 at 3:00 PM in 636 SEO