Mathematical Logic Weekly Seminar
Large Cardinals Beyond HOD
Large Cardinals Beyond HOD
Joan Bagaria i Pigrau, University of Barcelona
7 NOV 2024
14:00 - 16:00
I will present some recent results about new large cardinals that imply the set-theoretic universe is not HOD (the universe of Hereditarily Ordinal Definable sets). In particular, ultraexact cardinals are equiconsistent, modulo ZFC, with the existence of an I0 embedding, yet they imply that some successor cardinal is measurable in HOD. Moreover, the existence of an ultraexact cardinal together with an extendible cardinal below it is consistent with ZFC and refute Woodins HOD Conjecture. This is joint work with Juan Aguilera, Gabriel Goldberg, and Philipp Lucke.
Zoom room information:
https://us06web.zoom.us/j/81916335336?pwd=5zQT4lutMiBoY5Xp1pkFGtbqiaGozg.1
Meeting ID: 819 1633 5336
Passcode: 559618
Venue: Niavaran, Lecture Hall 1