Notre Dame Journal of Formal Logic

On the Indecomposability of ωn

Jared R. Corduan and François G. Dorais


We study the reverse mathematics of pigeonhole principles for finite powers of the ordinal ω. Four natural formulations are presented, and their relative strengths are compared. In the analysis of the pigeonhole principle for ω2, we uncover two weak variants of Ramsey’s theorem for pairs.

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

First available in Project Euclid: 24 September 2012

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Zentralblatt MATH identifier

Primary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35]
Secondary: 03F35: Second- and higher-order arithmetic and fragments [See also 03B30]

reverse mathematics indecomposability partition principles


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.

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