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arxiv 1910.11025 v6 pith:O4QHERAH submitted 2019-10-24 math.LO

Finiteness classes arising from Ramsey-theoretic statements in set theory without choice

classification math.LO
keywords setschoiceinfiniteramsey-theoreticstatementsappropriatelyarisingassume
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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.

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