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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.

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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