Activity: Participating in or organising an event types › Invited talk
Midlands Logic Seminar talk: AEC categoricity, category theory and large cardinals
Abstract: Classical model theory has many powerful results about models for first order theories, and in recent years there have been moves to try to mimic these results in a more general setting. But what is a good setting to do this in? The answer that has emerged from the model theory community is that of Abstract Elementary Classes (AECs); the answer from the category theory world is that of accessible categories. Recently Lieberman and Rosicky have shown that there is an intimate connection between these settings. They further show that a major recent result about AECs follows from known results about accessible categories - specifically, Boney's result that the Shelah Categoricity Conjecture for Successors holds assuming there is a proper class of strongly compact cardinals. I will talk about recent joint work with Rosicky, in which we improve these results, reducing the large cardinal assumption needed.