Journal of Symbolic Logic

Diagonal actions and Borel equivalence relations

Longyun Ding and Su Gao

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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.

Article information

J. Symbolic Logic, Volume 71, Issue 4 (2006), 1081-1096.

First available in Project Euclid: 20 November 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: Primary 04A15, 54H05, 22F05


Ding, Longyun; Gao, Su. Diagonal actions and Borel equivalence relations. J. Symbolic Logic 71 (2006), no. 4, 1081--1096. doi:10.2178/jsl/1164060445.

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