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Diagonal actions and Borel equivalence relations

Published online by Cambridge University Press:  12 March 2014

Longyun Ding  and
Su Gao
Longyun Ding
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, P. R. China, E-mail: dingly@nankai.edu.cn
Su Gao
Affiliation:
Department of Mathematics, Po Box 311430, University of North Texas, Denton, TX 76203, USA, E-mail: sgao@unt.edu
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Abstract

We investigate diagonal actions of Polish groups and the related intersection operator on closed subgroups of the acting group. The Borelness of the diagonal orbit equivalence relation is characterized and is shown to be connected with the Borelness of the intersection operator. We also consider relatively tame Polish groups and give a characterization of them in the class of countable products of countable abelian groups. Finally an example of a logic action is considered and its complexity in the Borel reducbility hierarchy determined.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 4 , December 2006 , pp. 1081 - 1096
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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