Michael Lieberman : Classification Theory for Accessible Categories

Posted by Joseph Zielinski , part of the Louise Hay Logic Seminar.

At

March 20, 2014, 3 p.m.

In

SEO 427

Abstract

We discuss recent joint work with Jiri Rosicky which seeks to extend a fragment of the classification theory of AECs to the more general framework of accessible categories, particularly for accessible categories with directed colimits: essentially AECs minus coherence. There are several pleasant surprises---a generalization of Boney's recent theorem on tameness under a large cardinal hypothesis follows from work of Makkai and Pare, and these categories admit a robust Ehrenfeucht-Mostowski functor which can be used to mimic certain constructions in AECs. On the other hand, this investigation also illuminates the areas and arguments where coherence is indispensable...