Translator Disclaimer
March 2013 Canonizing relations on nonsmooth sets
Clinton T. Conley
J. Symbolic Logic 78(1): 101-112 (March 2013). DOI: 10.2178/jsl.7801070

Abstract

We show that any symmetric, Baire measurable function from the complement of $E_0$ to a finite set is constant on an $E_0$-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 $E_0$-nonsmooth sets, this result is proved by relating $E_0$-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.

Citation

Download Citation

Clinton T. Conley. "Canonizing relations on nonsmooth sets." J. Symbolic Logic 78 (1) 101 - 112, March 2013. https://doi.org/10.2178/jsl.7801070

Information

Published: March 2013
First available in Project Euclid: 23 January 2013

zbMATH: 1361.03045
MathSciNet: MR3087064
Digital Object Identifier: 10.2178/jsl.7801070

Rights: Copyright © 2013 Association for Symbolic Logic

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.78 • No. 1 • March 2013
Back to Top