Hjorth, Greg and Kechris, Alexander S. (2001) Recent developments in the theory of Borel reducibility. Fundamenta Mathematicae, 170 (1-2). pp. 21-52. ISSN 0016-2736. https://resolver.caltech.edu/CaltechAUTHORS:20130610-142913085
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Abstract
Let E_0 be the Vitali equivalence relation and E_3 the product of countably many copies of E_0. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel equivalence relation E that is (Borel) reducible to E_3, either E is reducible to E_0 or else E_3 is reducible to E. Second, if E is a Borel equivalence relation induced by a Borel action of a closed subgroup of the infinite symmetric group that admits an invariant metric, then either E is reducible to a countable Borel equivalence relation or else E_3 is reducible to E. We also survey a number of results and conjectures concerning the global structure of reducibility on Borel equivalence relations.
Item Type: | Article | ||||||
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Additional Information: | © 2001 Institute of Mathematics, Polish Academy of Sciences. Research of the first author partially supported by NSF Grant DMS 96-22977. Research of the second author partially supported by NSF Grant DMS 96-19880. | ||||||
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Issue or Number: | 1-2 | ||||||
Classification Code: | 2000 Mathematics Subject Classification: Primary 03E15 | ||||||
Record Number: | CaltechAUTHORS:20130610-142913085 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130610-142913085 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 38881 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Tony Diaz | ||||||
Deposited On: | 19 Sep 2013 19:54 | ||||||
Last Modified: | 03 Oct 2019 05:01 |
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