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arXiv · 1111.1367

On the indecomposability of $\omega^n$

Jared R. Corduan·François G. Dorais
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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. 2011-11-06. On the indecomposability of $\omega^n$. https://doi.org/10.1215/00294527-1716784

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