Applications of large cardinals in AECs via category theory

Andrew Brooke-Taylor, University of Leeds. Part of the logic seminar series.

The theory of Abstract Elementary Classes attempts to generalise model theory away from the first order case, axiomatising the salient features of a good class of structures with a notion of elementary substructure. A key test question for this programme is whether the analogue of Morley\'s Theorem holds for AECs. Grossberg and VanDieren showed that one almost has it if your AEC is tame, and Boney subsequently showed that, assuming there is a proper class of strongly compact cardinals, every AEC is tame. I will present joint work with Jiri Rosicky where we reduce the large cardinal requirement for Boney's theorem. Our proof goes by way of improving an old result of Makkai and Paré on "powerful images" in category theory.

Andrew Brooke-Taylor, University of Leeds