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. doi:10.1016/S0168-0072(97)00049-3. https://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 | |||||||||
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| 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. | |||||||||
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| Subject Keywords: | Borel equivalence relations; Countable models; Infinite symmetric group | |||||||||
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| Issue or Number: | 1 | |||||||||
| Classification Code: | AMS classification: Primary: 04A15; 03A15; secondary: 03A20; 03C75; 20B30 | |||||||||
| DOI: | 10.1016/S0168-0072(97)00049-3 | |||||||||
| Record Number: | CaltechAUTHORS:20130517-142221264 | |||||||||
| Persistent URL: | https://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: | 09 Nov 2021 23:38 |
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