Activity: Participating in or organising an event types › Invited talk
CUNY Logic Workshop talk: Large cardinals, AECs and category theory
Abstract: Shelah’s Categoricity Conjecture is a central test question in the study of Abstract Elementary Classes (AECs) in model theory. Recently Boney has shown that under the assumption that sufficiently large strongly compact cardinals exist, the Shelah Categoricity Conjecture holds at successor cardinals. Lieberman and Rosicky have subsequently shown that AECs can be characterised in a very natural way in a category-theoretic setting, and with this perspective Boney’s result can actually be seen as a corollary of an old category-theoretic result of Makkai and Pare. Rosicky and I have now been able to improve upon this result of Makkai and Pare (and consequently Boney’s Theorem), obtaining it from α-strongly compact cardinals.