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Borel equivalence relations induced by actions of the symmetric group

Hjorth, Greg and Kechris, Alexander S. and Louveau, Alain (1998) Borel equivalence relations induced by actions of the symmetric group. Annals of Pure and Applied Logic, 92 (1). pp. 63-112. ISSN 0168-0072. http://resolver.caltech.edu/CaltechAUTHORS:20130517-142221264

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Abstract

We consider Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank. We relate the descriptive complexity of the equivalence relation to the nature of its complete invariants. A typical theorem is that E is potentially Π^0_3 iff the invariants are countable sets of reals, it is potentially Π^0_4 iff the invariants are countable sets of countable sets of reals, and so on. The proofs use various techniques, including Vaught transforms, changing topologies, and the Scott analysis of countable models.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/S0168-0072(97)00049-3DOIUNSPECIFIED
http://www.sciencedirect.com/science/article/pii/S0168007297000493PublisherUNSPECIFIED
Additional Information:© 1998 Published by Elsevier Science B.V. Received 16 December 1996; accepted 11 October 1997. Research partially supported by NSF Grant DMS-9317509.
Funders:
Funding AgencyGrant Number
NSFDMS-9317509
Subject Keywords:Borel equivalence relations; Countable models; Infinite symmetric group
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR1624736
Classification Code:AMS classification: Primary: 04A15; 03A15; secondary: 03A20; 03C75; 20B30
Record Number:CaltechAUTHORS:20130517-142221264
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130517-142221264
Official Citation:Greg Hjorth, Alexander S. Kechris, Alain Louveau, Borel equivalence relations induced by actions of the symmetric group, Annals of Pure and Applied Logic, Volume 92, Issue 1, 11 March 1998, Pages 63-112, ISSN 0168-0072, 10.1016/S0168-0072(97)00049-3. (http://www.sciencedirect.com/science/article/pii/S0168007297000493)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38569
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:20 May 2013 16:07
Last Modified:22 May 2013 22:49

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