Dave Marker : Borel complexity of isomorphism for theories with many types

Posted by Matthias Aschenbrenner , part of the Logic Seminar.

At

Sept. 5, 2006, 4 p.m.

In

SEO 427

Abstract

If E is a Borel equivalence relation with countably many classes, then there is an infinitary sentence $\phi$ such that E is Borel bi-reducible to the isomorphism relation for $\phi$. Kechris and Hjorth asked if the same was true for first order theories. We show that if a theory has uncountably many types, then the isomorphism relation is more complicated than any Borel equivalence relation with countably many classes.