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arXiv · 1512.02954

Dickson's lemma and weak Ramsey theory

Yasuhiko Omata·Florian Pelupessy
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Abstract

We explore the connections between Dickson's lemma and weak Ramsey theory. We show that a weak version of the Paris--Harrington principle for pairs in $c$ colors and miniaturized Dickson's lemma for $c$-tuples are equivalent over $\mathsf{RCA}_0^{\ast}$. Furthermore, we look at a cascade of consequences for several variants of weak Ramsey's theorem.

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Yasuhiko Omata, Florian Pelupessy. 2017-10-03. Dickson's lemma and weak Ramsey theory. https://doi.org/10.1007/s00153-018-0642-3

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