20230717 
15:3016:30 
20230717,15:3016:30  LR1 (A31 3F) 
0717 Afternoon Lecture Room 1 (A31 3F)

Speaker 
The axiom V = UltimateL and Goldberg's Ultrapower axiom The axiom V = UltimateL is the leading candidate for the maximum possible generalization of Gödel's axiom, V = L. The Ultimate Program is the program to show that the axiom V = UltimateL is not refuted by large cardinal axioms. This involves a series a rather specific conjectures, which is the family of UltimateL Conjectures. A key part of this program is to develop the structure theory of UltimateL. Goldberg's Ultrapower Axiom holds in all the current generalizations of L which have been constructed in the Inner Model Program which is another major program of Set Theory to identify generalizations of L. The Ultrapower Axiom has deep structural consequences in the context of large cardinal axioms. For example, it implies the Generalized Continuum Hypothesis must hold above the least strongly compact cardinal and it implies the least strongly compact cardinal is supercompact. By recent theorem, if V = UltimateL then the Ultrapower Axiom holds. The unexpected feature here is that this can be proved without settling the UltimateL Conjectures.
