Logic at UC Berkeley Conference: Absolutely ordinal definable sets

Seminar | May 5 | 9:30-10:45 a.m. | 141 McCone Hall

 John Steel, UC Berkeley

 Department of Mathematics

Set theorists have discovered many mutually incompatible natural theories extending ZFC. One can hope that these incompatibilities will be resolved by interpreting all such theories in a useful common framework theory. There is a promising candidate for such a framework theory. Its crucial axiom, “Axiom H”, asserts that V looks like the collection of hereditarily ordinal definable sets in a model of the Axiom of Determinacy. Recent work on the theory of HOD in models of the Axiom of Determinacy adds evidence for Axiom H.