Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-16T23:12:00.286Z Has data issue: false hasContentIssue false
  • English
  • Français

Borel equivalence relations which are highly unfree

Published online by Cambridge University Press:  12 March 2014

Greg Hjorth
Greg Hjorth*
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Parkville 3010 Victoria, Australia, E-mail: [email protected], URL: http://www.math.ucla.edu/~greg/
Get access Rights & Permissions [Opens in a new window]

Abstract

There is an ergodic, measure preserving, countable Borel equivalence relation E on a standard Borel probability space (X, μ) such that E∣c is not essentially free on any conull C ⊂ X.

Keywords

Ergodic theoryBorel equivalence relationsfree group actionsBorel reducibility
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 4 , December 2008 , pp. 1271 - 1277
Copyright
Copyright © Association for Symbolic Logic 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Adams, S., An equivalence relation that is not freely generated, Proceedings of American Mathematical Society, vol. 102 (1988), pp. 565–566.CrossRefGoogle Scholar
[2]Feldman, J. and Moore, C.C., Ergodic equivalence relations, cohomology, and von Neumann algebras. I, II, Transactions of American Mathematical Society, vol. 234 (1977), pp. 289–324, 325–359.CrossRefGoogle Scholar
[3]Furman, A., Orbit equivalence rigidity, Annals of Mathematics, vol. 150 (1999).CrossRefGoogle Scholar
[4]Hjorth, G. and Kechris, A.S., Rigidity theorems for actions of product groups and countable Borel equivalence relations, vol. 177, Memoirs of the AMS, 2005.Google Scholar
[5]Jackson, S., Kechris, A.S., and Louveau, A., Countable Borel equivalence relations, Journal of Mathematical Logic, vol. 2 (2002), no. 1, pp. 1–80.CrossRefGoogle Scholar
[6]Popa, S., Cocycle and orbit equivalence superrigidity for Bernoulli actions of Kazhdan groups, preprint.Google Scholar
[7]Thomas, S., Popa superrigidity and countable Borel equivalence relations, preprint.Google Scholar
[8]Zimmer, R.J., Ergodic theory and semisimple groups, Birkhäuser, Basel, 1984.CrossRefGoogle Scholar