Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Selection theorems and treeability


Author: Greg Hjorth
Journal: Proc. Amer. Math. Soc. 136 (2008), 3647-3653
MSC (2000): Primary 03E15
Published electronically: May 22, 2008
MathSciNet review: 2415050
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that domains of non-trivial $ \Sigma^1_1$ trees have $ \Delta^1_1$ members. Using this, we show that smooth treeable equivalence relations have Borel transversals, and essentially countable treeable equivalence relations have Borel complete countable sections. We show also that treeable equivalence relations which are ccc idealistic, measured, or generated by a Borel action of a Polish group have Borel complete countable sections.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E15

Retrieve articles in all journals with MSC (2000): 03E15


Additional Information

Greg Hjorth
Affiliation: Department of Mathematics and Statistics, University of Melbourne, Parkville, 3010 Victoria, Australia
Email: greg.hjorth@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09548-8
PII: S 0002-9939(08)09548-8
Keywords: Borel equivalence relations, treeable equivalence relations, selection theorem, uniformization
Received by editor(s): November 20, 2006
Published electronically: May 22, 2008
Additional Notes: The author gratefully acknowledges partial support from the Australian Research Council.
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.