Borel equivalence relations and classifications of countable models
Using the theory of Borel equivalence relations we analyze the isomorphism relation on the countable models of a theory and develop a framework for measuring the complexity of possible complete invariants for isomorphism.
© 1996 Elsevier Science B.V. Received 25 July 1995. Communicated by T. Jech. Research partially supported by NSF Grant DMS-9317509. We would like to thank A. Hales and G. Melles for many useful discussions concerning the subject matter of this paper, which led, in particular, to our formulation of the cocycle property for actions and motivated the proof that it is equivalent (in the case of logic actions) to the existence of canonical models.