Gabriel Goldberg : Strong compactness and the $\omega$-club filter.

Posted by Filippo Calderoni , part of the Logic Seminar.

At

April 27, 2021, 4 p.m.

In

Zoom

Abstract

I'll discuss some ideas relating strong compactness, club filters, and inner models, with two applications: first, a generalization of Woodin's HOD dichotomy that applies to any inner model with access to the \(\omega\)-club filter on each ordinal of uncountable cofinality, and second, an analysis of strong compactness in the HODs of models satisfying either the Axiom of Determinacy or choiceless large cardinal assumptions.