Finite Ultrahomogeneous Structures

Leo Harrington

University of California, Berkeley

This will be a presentation of the Cherlin-Lachlan classification of finite ultrahomogeneous structures in a fixed finite relational language. (Here ultrahomogeneous means: quantifier-free homogeneous). This result relies on the classification of finite simple groups to show that the theory (of all finite ultrahomogeneous structures in a fixed finite relational language) is omega-stable of finite rank. This presentation will not deal with that part of the argument, but will rather assume it and then present how Lachlan's shrinking technique leads to a classification.