Hindman's Theorem in the hierarchy of Choice Principles
Abstract
In the context of $\mathsf{ZF}$, 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 $\mathsf{AC}$.
 Publication:

arXiv eprints
 Pub Date:
 March 2022
 arXiv:
 arXiv:2203.06156
 Bibcode:
 2022arXiv220306156F
 Keywords:

 Mathematics  Logic;
 Primary 03E25;
 Secondary 03E35;
 03E30;
 03E65;
 03E02;
 03E05
 EPrint:
 17 pages, 2 figures