English

Dickson's lemma and weak Ramsey theory

Logic 2018-08-03 v3

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 cc colors and miniaturized Dickson's lemma for cc-tuples are equivalent over RCA0\mathsf{RCA}_0^{\ast}. Furthermore, we look at a cascade of consequences for several variants of weak Ramsey's theorem.

Keywords

Cite

@article{arxiv.1512.02954,
  title  = {Dickson's lemma and weak Ramsey theory},
  author = {Yasuhiko Omata and Florian Pelupessy},
  journal= {arXiv preprint arXiv:1512.02954},
  year   = {2018}
}
R2 v1 2026-06-22T12:05:29.972Z