English

Hindman's Theorem in the hierarchy of Choice Principles

Logic 2024-01-30 v3

Abstract

In the context of ZF\mathsf{ZF}, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the AC\mathsf{AC}.

Keywords

Cite

@article{arxiv.2203.06156,
  title  = {Hindman's Theorem in the hierarchy of Choice Principles},
  author = {David J. Fernández-Bretón},
  journal= {arXiv preprint arXiv:2203.06156},
  year   = {2024}
}

Comments

17 pages, 2 figures. Last batch of minor changes to accurately reflect the final published version of the paper