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OPEN QUESTIONS ABOUT RAMSEY-TYPE STATEMENTS IN REVERSE MATHEMATICS

Published online by Cambridge University Press:  05 July 2016

LUDOVIC PATEY
LUDOVIC PATEY*
Affiliation:
LABORATOIRE PPS UNIVERSITÉ PARIS DIDEROT PARIS, FRANCEE-mail: ludovic.patey@computability.frURL: http://www.ludovicpatey.com
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Abstract

Ramsey’s theorem states that for any coloring of the n-element subsets of ℕ with finitely many colors, there is an infinite set H such that all n-element subsets of H have the same color. The strength of consequences of Ramsey’s theorem has been extensively studied in reverse mathematics and under various reducibilities, namely, computable reducibility and uniform reducibility. Our understanding of the combinatorics of Ramsey’s theorem and its consequences has been greatly improved over the past decades. In this paper, we state some questions which naturally arose during this study. The inability to answer those questions reveals some gaps in our understanding of the combinatorics of Ramsey’s theorem.

Keywords

Reverse mathematicsRamsey’s theoremcohesivenessopen questions
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 22 , Issue 2 , June 2016 , pp. 151 - 169
Copyright
Copyright © The Association for Symbolic Logic 2016 

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