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A Glimm-Effros dichotomy for Borel equivalence relations

Harrington, L. A. and Kechris, A. S. and Louveau, A. (1990) A Glimm-Effros dichotomy for Borel equivalence relations. Journal of the American Mathematical Society, 3 (4). pp. 903-928. ISSN 0894-0347. doi:10.1090/S0894-0347-1990-1057041-5.

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A basic dichotomy concerning the structure of the orbit space of a transformation group has been discovered by Glimm [G12] in the locally compact group action case and extended by Effros [E 1, E2] in the Polish group action case when additionally the induced equivalence relation is Fσ. It is the purpose of this paper to extend the Glimm-Effros dichotomy to the very general context of an arbitrary Borel equivalence relation (not even necessarily induced by a group action). Despite the totally classical descriptive set-theoretic nature of our result, our proof requires the employment of methods of effective descriptive set theory and thus ultimately makes crucial use of computability (or recursion) theory on the integers.

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Additional Information:© 1990 American Mathematical Society. Received by the editors March 2, 1990. The first and second authors were partially supported by NSF grants.
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MathSciNet ReviewMR1057041
Issue or Number:4
Classification Code:1980 Mathematics Subject Classification (1985 Revision). Primary 03E15, 04A15, 46L05, 28099
Record Number:CaltechAUTHORS:20130521-131913642
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38609
Deposited By: Jason Perez
Deposited On:22 May 2013 21:03
Last Modified:09 Nov 2021 23:38

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