On the Indecomposability of $\omega^{n}$

Notre Dame Journal of Formal Logic 53 (3):373-395 (2012)
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Abstract

We study the reverse mathematics of pigeonhole principles for finite powers of the ordinal $\omega$ . Four natural formulations are presented, and their relative strengths are compared. In the analysis of the pigeonhole principle for $\omega^{2}$ , we uncover two weak variants of Ramsey’s theorem for pairs

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References found in this work

On the Strength of Ramsey's Theorem.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.
A cohesive set which is not high.Carl Jockusch & Frank Stephan - 1993 - Mathematical Logic Quarterly 39 (1):515-530.
The polarized Ramsey’s theorem.Damir D. Dzhafarov & Jeffry L. Hirst - 2009 - Archive for Mathematical Logic 48 (2):141-157.

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