Finiteness classes arising from Ramsey-theoretic statements in set theory without choice
arXiv:1910.11025 · doi:10.1016/j.apal.2021.102961
Abstract
We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We obtain very precise information as to where such sets are located within the hierarchy of infinite Dedekind-finite sets.
23 pages, 1 figure+1 picture. A few typos corrected, and some references updated, as compared to the previous version