# David Fernández-Bretón: Finiteness classes arising from Ramsey-theoretic statements in set theory without choice

Talk held by David Fernández-Bretón (KGRC) at the KGRC seminar on 2018-10-04. The recorded talk is available here.

Abstract: In the absence of the Axiom of Choice, there may be infinite sets for which certain Ramsey-theoretic statements – such as Ramsey’s or (appropriately phrased) Hindman’s theorem – fail. In this talk, we will analyse the existence of such sets, and their precise location within the hierarchy of infinite Dedekind-finite sets; independence proofs will be carried out using the Fränkel-Mostowski technique of permutation models.

This is joint work with Joshua Brot and Mengyang Cao.

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