Notre Dame Journal of Formal Logic

On the Indecomposability of ωn

Jared R. Corduan and François G. Dorais

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 24 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1348524117

Digital Object Identifier
doi:10.1215/00294527-1716784

Mathematical Reviews number (MathSciNet)
MR2981014

Zentralblatt MATH identifier
1260.03017

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

Keywords
reverse mathematics indecomposability partition principles

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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