English

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 ACA0+\mathsf{ACA}^{+}_0.

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

R2 v1 2026-06-25T01:14:13.147Z