Event Detail

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.