## Logic Seminar

Gabriel Goldberg

UC Berkeley

Strong compactness and the $\omega$-club filter.

**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.

Tuesday April 27, 2021 at 4:00 PM in Zoom