Some applications of the Adams-Kechris technique
Author:
Su Gao
Journal:
Proc. Amer. Math. Soc. 130 (2002), 863-874
MSC (1991):
Primary 03E15
DOI:
https://doi.org/10.1090/S0002-9939-01-06082-8
Published electronically:
June 20, 2001
MathSciNet review:
1866043
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
347662
Email:
sugao@its.caltech.edu
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
