Matt Foreman: Inner models for huge cardinals and Strong Chang's Conjecture

Week 1, Thursday June 18, 08:50-09:40

Chang's Conjectures are strengthenings of the Lowenheim-Skolem theorem. Given an arbitrary structure A they ask for an elementary substructure B where the cardinalities of the intersections of B with various predicates are specified in advance.
If A is well-founded one could also ask that the transitive collapse of B be large; i.e. that B have strong condensation properties. In this talk a strong Chang's Conjecture of this form is presented. The consistency strength of this Chang's Conjecture holding at omega_3 is between a 2-huge and a huge cardinal.