On the Indecomposability of ωn

Jared R. Corduan; François G. Dorais

doi:10.1215/00294527-1716784

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Home > Journals > Notre Dame J. Formal Logic > Volume 53 > Issue 3 > Article

2012 On the Indecomposability of

\omega^{n}

Jared R. Corduan, François G. Dorais

Notre Dame J. Formal Logic 53(3): 373-395 (2012). DOI: 10.1215/00294527-1716784

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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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Jared R. Corduan. François G. Dorais. "On the Indecomposability of $\omega^{n}$ ." Notre Dame J. Formal Logic 53 (3) 373 - 395, 2012. https://doi.org/10.1215/00294527-1716784