ABSTRACT
The study of general analytic equivalence relations is a very important and yet challenging subject. In this chapter we will discuss general dichotomy theorems for analytic equivalence relations, universal analytic equivalence relations, and other examples of analytic but non-Borel equivalence relations. Orbit equivalence relations of Polish group actions are in general analytic, and often non-Borel, and therefore provide many interesting examples and opportunities of applications of general theorems. The Borel reducibility hierarchy for analytic equivalence relations is more complicated than the one for Borel equivalence relations.
