The automorphic Borel amalgamation property
We show that, in many cases, there is a Borel reduction from the isomorphism relation on a given Fraïssé class to the conjugacy relation on the automorphism group of the Fraïssé limit. Hence, if the former is Borel complete, then so is the latter. The key property is a functorial, Borel form of amalgamation. All relevant notions about Borel redicibility and Fraïssé classes will be defined.
Paul Ellis is currently an assistant professor at Manhattanville College. He received his doctorate from Rutgers University under the supervision of Simon Thomas in 2009. He has previously held an assistant professorship at the University of Connecticut. His research interests include logic, set theory, and Borel equivalence relations.