On the indecomposability of $ω^n$

Jared R. Corduan, François G. Dorais

Published 2011-11-06Version 1

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.