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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
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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.

Information

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

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References

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