Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-11T01:06:25.804Z Has data issue: false hasContentIssue false
  • English
  • Français

Canonizing relations on nonsmooth sets

Published online by Cambridge University Press:  12 March 2014

Clinton T. Conley
Clinton T. Conley*
Affiliation:
Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Straße 25, 1090 Wien, Austria
*
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA, E-mail: clintonc@math.cornell.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that any symmetric, Baire measurable function from the complement of E0 to a finite set is constant on an E0-nonsmooth square. A simultaneous generalization of Galvin's theorem that Baire measurable colorings admit perfect homogeneous sets and the Kanovei-Zapletal theorem canonizing Borel equivalence relations on E0-nonsmooth sets, this result is proved by relating E0-nonsmooth sets to embeddings of the complete binary tree into itself and appealing to a version of Hindman's theorem on the complete binary tree. We also establish several canonization theorems which follow from the main result.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 1 , March 2013 , pp. 101 - 112
Copyright
Copyright © Association for Symbolic Logic 2013

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]Harrington, L.A., Kechris, A.S., and Louveau, A., A Glimm-Effros dichotomy for Borel equivalence relations, Journal of the American Mathematical Society, vol. 3 (1990), no. 4, pp. 903–928.CrossRefGoogle Scholar
[2]Kechris, A.S., Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, 1995.CrossRefGoogle Scholar
[3]Miller, B.D., The Kanovei-Zapletal canonization, Set theory and its applications (Babinkostova, L., Caicedo, A.E., Geschke, S., and Scheepers, M., editors), Contemporary Mathematics, vol. 533, American Mathematical Society, Providence, 2011, pp. 281–286.CrossRefGoogle Scholar
[4]Todorcevic, Stevo, Introduction to Ramsey spaces, Annals of Mathematics Studies, vol. 174, Princeton University Press, Princeton, NJ, 2010.CrossRefGoogle Scholar