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 colors and miniaturized Dickson's lemma for -tuples are equivalent over . 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}
}