DOCUMENTA MATHEMATICA, Extra Volume ICM II (1998), 23-32

Greg Hjorth

Title: When is an Equivalence Relation Classifiable?

One finds in certain branches of analysis the idea that a classifiable equivalence relation is one for which we can assign points in a very concrete space as a complete invariant. Results by Effros, Glimm, and Mackey, and then later Harrington, Kechris, and Louveau, have given a thorough analysis of when such a classification is possible. In the last few years a similar analysis has been undertaken by descriptive set theorists regarding when an equivalence relation is classifiable by {\it countable structures considered up to isomorphism}. There is a kind of parallel theory of which equivalence relations can be assigned countable structures as complete invariants.

1991 Mathematics Subject Classification: 04A15

Keywords and Phrases: Equivalence relations, effective cardinality, classification, Polish group actions.

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