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June 2009 Ramsey's theorem and cone avoidance
Damir D. Dzhafarov, Carl G Jockusch, Jr.
J. Symbolic Logic 74(2): 557-578 (June 2009). DOI: 10.2178/jsl/1243948327

Abstract

It was shown by Cholak, Jockusch, and Slaman that every computable 2-coloring of pairs admits an infinite low2 homogeneous set H. We answer a question of the same authors by showing that H may be chosen to satisfy in addition C ≰T H, where C is a given noncomputable set. This is shown by analyzing a new and simplified proof of Seetapun's cone avoidance theorem for Ramsey's theorem. We then extend the result to show that every computable 2-coloring of pairs admits a pair of low2 infinite homogeneous sets whose degrees form a minimal pair.

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Damir D. Dzhafarov. Carl G Jockusch, Jr.. "Ramsey's theorem and cone avoidance." J. Symbolic Logic 74 (2) 557 - 578, June 2009. https://doi.org/10.2178/jsl/1243948327

Information

Published: June 2009
First available in Project Euclid: 2 June 2009

zbMATH: 1166.03021
MathSciNet: MR2518811
Digital Object Identifier: 10.2178/jsl/1243948327

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 2 • June 2009
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