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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some applications of the Adams-Kechris technique


Author: Su Gao
Journal: Proc. Amer. Math. Soc. 130 (2002), 863-874
MSC (1991): Primary 03E15
Published electronically: June 20, 2001
MathSciNet review: 1866043
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Abstract: We analyze the technique used by Adams and Kechris (2000) to obtain their results about Borel reducibility of countable Borel equivalence relations. Using this technique, we show that every $\boldsymbol{\Sigma}^1_1$ equivalence relation is Borel reducible to the Borel bi-reducibility of countable Borel equivalence relations. We also apply the technique to two other classes of essentially uncountable Borel equivalence relations and derive analogous results for the classification problem of Borel automorphisms.


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Additional Information

Su Gao
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: sugao@its.caltech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06082-8
PII: S 0002-9939(01)06082-8
Keywords: Borel equivalence relations, Borel (bi-)reducibility
Received by editor(s): February 10, 2000
Received by editor(s) in revised form: August 13, 2000, and August 23, 2000
Published electronically: June 20, 2001
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2001 American Mathematical Society