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The classification of hypersmooth Borel equivalence relations

Kechris, Alexander S. and Louveau, Alain (1997) The classification of hypersmooth Borel equivalence relations. Journal of the American Mathematical Society, 10 (1). pp. 215-242. ISSN 0894-0347. doi:10.1090/S0894-0347-97-00221-X.

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This paper is a contribution to the study of Borel equivalence relations in standard Borel spaces, i.e., Polish spaces equipped with their Borel structure. A class of such equivalence relations which has received particular attention is the class of hyperfinite Borel equivalence relations. These can be defined as the increasing unions of sequences of Borel equivalence relations all of whose equivalence classes are finite or, as it turns out, equivalently those induced by the orbits of a single Borel auto-morphism. Hyperfinite equivalence relations have been classified in [DJK], under two notions of equivalence, Borel bi-reducibility, and Borel isomorphism.

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Additional Information:© 1997 American Mathematical Society. Received by the editors September 1, 1994 and, in revised form, June 11, 1996. The first author's research was partially supported by NSF Grant DMS-9317509.
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Subject Keywords:Borel equivalence relations, hypersmooth, dichotomy theorems.
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MathSciNet review1396895
Issue or Number:1
Classification Code:1991 Mathematics Subject Classification: Primary 04A15, 03E15
Record Number:CaltechAUTHORS:20130521-133826211
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38613
Deposited By: Tony Diaz
Deposited On:23 May 2013 15:51
Last Modified:09 Nov 2021 23:38

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