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.