Some applications of the Adams-Kechris technique
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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.References
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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
- 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.
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 863-874
- MSC (1991): Primary 03E15
- DOI: https://doi.org/10.1090/S0002-9939-01-06082-8
- MathSciNet review: 1866043