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Dickson’s lemma and weak Ramsey theory
Archive for Mathematical Logic 58 (3-4):413-425 (2019)
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 \. Furthermore, we look at a cascade of consequences for several variants of weak Ramsey’s theorem.Links
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References found in this work
Ordinal numbers and the Hilbert basis theorem.Stephen G. Simpson - 1988 - Journal of Symbolic Logic 53 (3):961-974.
On principles between ∑1- and ∑2-induction, and monotone enumerations.Alexander P. Kreuzer & Keita Yokoyama - 2016 - Journal of Mathematical Logic 16 (1):1650004.
Factorization of polynomials and °1 induction.S. G. Simpson - 1986 - Annals of Pure and Applied Logic 31:289.
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