Carlson-Simpson's lemma and applications in reverse mathematics
Logic
2023-05-11 v2
Abstract
We study the reverse mathematics of infinitary extensions of the Hales-Jewett theorem, due to Carlson and Simpson. These theorems have multiple applications in Ramsey's theory, such as the existence of finite big Ramsey numbers for the triangle-free graph, or the Dual Ramsey theorem. We show in particular that the Open Dual Ramsey theorem holds in .
Cite
@article{arxiv.2207.12828,
title = {Carlson-Simpson's lemma and applications in reverse mathematics},
author = {Paul-Elliot Anglès d'Auriac and Bastien Mignoty and Lu Liu and Ludovic Patey},
journal= {arXiv preprint arXiv:2207.12828},
year = {2023}
}
Comments
13 pages