CaltechAUTHORS
  A Caltech Library Service

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. https://resolver.caltech.edu/CaltechAUTHORS:20130521-131913642

[img]
Preview
PDF - Published Version
See Usage Policy.

2926Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20130521-131913642

Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1090/S0894-0347-1990-1057041-5 DOIUNSPECIFIED
http://www.ams.org/journals/jams/1990-03-04/S0894-0347-1990-1057041-5/home.htmlPublisherUNSPECIFIED
Additional Information:© 1990 American Mathematical Society. Received by the editors March 2, 1990. The first and second authors were partially supported by NSF grants.
Funders:
Funding AgencyGrant Number
NSFUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR1057041
Issue or Number:4
Classification Code:1980 Mathematics Subject Classification (1985 Revision). Primary 03E15, 04A15, 46L05, 28099
Record Number:CaltechAUTHORS:20130521-131913642
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130521-131913642
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38609
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:22 May 2013 21:03
Last Modified:03 Oct 2019 04:58

Repository Staff Only: item control page