Dickson's lemma and weak Ramsey theory

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.

References in corpus (1)

• Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma