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.

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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

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Vol.78 • No. 1 • March 2013
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