Open Access
2011 Stable Ramsey's Theorem and Measure
Damir D. Dzhafarov
Notre Dame J. Formal Logic 52(1): 95-112 (2011). DOI: 10.1215/00294527-2010-039


The stable Ramsey's theorem for pairs has been the subject of numerous investigations in mathematical logic. We introduce a weaker form of it by restricting from the class of all stable colorings to subclasses of it that are nonnull in a certain effective measure-theoretic sense. We show that the sets that can compute infinite homogeneous sets for nonnull many computable stable colorings and the sets that can compute infinite homogeneous sets for all computable stable colorings agree below $\emptyset'$ but not in general. We also answer the analogs of two well-known questions about the stable Ramsey's theorem by showing that our weaker principle does not imply COH or WKL0 in the context of reverse mathematics.


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Damir D. Dzhafarov. "Stable Ramsey's Theorem and Measure." Notre Dame J. Formal Logic 52 (1) 95 - 112, 2011.


Published: 2011
First available in Project Euclid: 13 December 2010

zbMATH: 1217.03019
MathSciNet: MR2747165
Digital Object Identifier: 10.1215/00294527-2010-039

Primary: 03D32 , 03D80 , 03F35 , 05D10

Keywords: effective measure theory , Ramsey's theorem , reverse mathematics

Rights: Copyright © 2011 University of Notre Dame

Vol.52 • No. 1 • 2011
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