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arXiv · 1910.11025

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

Joshua Brot·Mengyang Cao·David Fernández-Bretón
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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.

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Joshua Brot, Mengyang Cao, David Fernández-Bretón. 2019-10-24. Finiteness classes arising from Ramsey-theoretic statements in set theory without choice. https://doi.org/10.1016/j.apal.2021.102961

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