Notre Dame Journal of Formal Logic

On the Indecomposability of $\omega^{n}$

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 53, Number 3 (2012), 373-395.

Dates
First available in Project Euclid: 24 September 2012

https://projecteuclid.org/euclid.ndjfl/1348524117

Digital Object Identifier
doi:10.1215/00294527-1716784

Mathematical Reviews number (MathSciNet)
MR2981014

Zentralblatt MATH identifier
1260.03017

Citation

Corduan, Jared R.; Dorais, François G. On the Indecomposability of $\omega^{n}$. Notre Dame J. Formal Logic 53 (2012), no. 3, 373--395. doi:10.1215/00294527-1716784. https://projecteuclid.org/euclid.ndjfl/1348524117

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