The HOD conjecture and its failure

Gabriel Goldberg (UC, Berkeley)

Jun 28. 2024, 09:15 — 10:00

The subject of this tutorial is Woodin's HOD conjecture, one of the most prominent open problems in pure set theory. We begin with a proof of his HOD dichotomy theorem along with an improvement of the speaker's reducing the large cardinal hypothesis from an extendible to a strongly compact cardinal. Following this, we mostly discuss the implications of the failure of the HOD conjecture, especially $\omega$-strongly measurable cardinals and a condition under which such cardinals are locally supercompact in $\HOD$.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Determinacy, Inner Models and Forcing Axioms (Workshop)
Organizer(s):
Sandra Müller (TU Vienna)
Grigor Sargsyan (Polish Academy of Science, Warsaw)
Ralf Schindler (WWU Münster)
John Steel (UC, Berkeley)