On the indecomposability of $\omega^n$
By J. Corduan and F. G. Dorais
Notre Dame Journal of Formal Logic 53 (2012), 373–395
We study the reverse mathematics of pigeonhole principles for finite powers of the ordinal . Four natural formulations are presented and their relative strengths are compared. In the analysis of the pigeonhole principle for , we uncover two weak variants of Ramsey’s Theorem for pairs.