Journal of Symbolic Logic

Diagonal actions and Borel equivalence relations

Longyun Ding and Su Gao

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

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

Dates
First available in Project Euclid: 20 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1164060445

Digital Object Identifier
doi:10.2178/jsl/1164060445

Mathematical Reviews number (MathSciNet)
MR2275849

Zentralblatt MATH identifier
1109.03050

Subjects
Primary: Primary 04A15, 54H05, 22F05

Citation

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


Export citation

References

  • H. Becker and A. S. Kechris, The descriptive set theory of Polish group actions, London Mathematical Society Lecture Notes Series, vol. 232, Cambridge University Press, 1996.
  • G. Hjorth and A. S. Kechris, Borel equivalence relations and classifications of countable models, Annals of Pure and Applied Logic, vol. 82 (1996), pp. 221--272.
  • G. Hjorth, A. S. Kechris, and A. Louveau, Borel equivalence relations induced by actions of the symmetric group, Annals of Pure and Applied Logic, vol. 92 (1998), pp. 63--112.
  • A. S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, 1995.
  • D. J. S. Robinson, A course in the theory of groups, Graduate Texts in Mathematics, vol. 80, Springer, 1996.
  • R. Sami, Polish group actions and the Vaught conjecture, Transactions of the American Mathematical Society, vol. 341 (1994), pp. 335--353.
  • Y. S. Samoilenko, Spectral theory of families of self-adjoint operators, Mathematics and Its Applications (Soviet Series), vol. 57, Kluwer Academic Publishers, 1991.
  • S. Solecki, Equivalence relations induced by actions of Polish groups, Transactions of the American Mathematical Society, vol. 347 (1995), pp. 4765--4777.