Adams, Scot and Kechris, Alexander S. (2000) Linear algebraic groups and countable Borel equivalence relations. Journal of the American Mathematical Society, 13 (4). pp. 909-943. ISSN 0894-0347. doi:10.1090/S0894-0347-00-00341-6. https://resolver.caltech.edu/CaltechAUTHORS:20130524-130949007
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Abstract
This paper is a contribution to the study of Borel equivalence relations on standard Borel spaces (i.e., Polish spaces equipped with their Borel structure). In mathematics one often deals with problems of classification of objects up to some notion of equivalence by invariants. Frequently these objects can be viewed as elements of a standard Borel space X and the equivalence turns out to be a Borel equivalence relation E on X. A complete classification of X up to E consists of finding a set of invariants I and a map c : X → I such that xEy ⇔ c(x) = c(y). For this to be of any interest both I and c must be explicit or definable and as simple and concrete as possible. The theory of Borel equivalence relations studies the set-theoretic nature of possible invariants and develops a mathematical framework for measuring the complexity of such classification problems.
Item Type: | Article | |||||||||
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Additional Information: | © 2000 American Mathematical Society. Received by the editors March 27, 1999 and, in revised form, April 21, 2000. Article electronically published on June 23, 2000. The first author's research was partially supported by NSF Grant DMS 9703480. The second author's research was partially supported by NSF Grant DMS 9619880 and a Visiting Miller Research Professorship at U.C. Berkeley. | |||||||||
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Issue or Number: | 4 | |||||||||
Classification Code: | 2000 MSC: Primary 03E15; Secondary 37A20 | |||||||||
DOI: | 10.1090/S0894-0347-00-00341-6 | |||||||||
Record Number: | CaltechAUTHORS:20130524-130949007 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130524-130949007 | |||||||||
Official Citation: | Adams, Scott and Kechris, Alexander S. (2000) Linear algebraic groups and countable Borel equivalence relations. Journal of the American Mathematical Society, 13 (4). pp. 909-943. | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 38668 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | Tony Diaz | |||||||||
Deposited On: | 29 May 2013 22:37 | |||||||||
Last Modified: | 09 Nov 2021 23:39 |
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