Open questions about Ramsey-type statements in reverse mathematics

Bulletin of Symbolic Logic 22 (2):151-169 (2016)
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Abstract

Ramsey’s theorem states that for any coloring of then-element subsets of ℕ with finitely many colors, there is an infinite setHsuch that alln-element subsets ofHhave 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.

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Citations of this work

Ramsey-Like Theorems and Moduli of Computation.Ludovic Patey - 2022 - Journal of Symbolic Logic 87 (1):72-108.

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References found in this work

Open Questions in Reverse Mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
On the Strength of Ramsey's Theorem.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.
Ramsey's Theorem and Recursion Theory.Carl G. Jockusch - 1972 - Journal of Symbolic Logic 37 (2):268-280.

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