# François G. Dorais

### 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 $\omega$. 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.