2021
DOI: 10.48550/arxiv.2111.05099
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Coalgebraic methods for Ramsey degrees of unary algebras

Abstract: In this paper we are interested in the existence of small and big Ramsey degrees of classes of finite unary algebras in arbitrary (not necessarily finite) algebraic language Ω. We think of unary algebras as M -sets where M = Ω * is the free monoid of words over the alphabet Ω and show that for an arbitrary monoid M (finite or infinite) the class of all finite M -sets has finite small Ramsey degrees. This immediately implies that the class of all finite G-sets, where G is an arbitrary group (finite or infinite)… Show more

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