Kőnig = Ramsey, A compactness lemma for Ramsey categories

Published 15 Aug 2025 in math.CO | (2508.11465v1)

Abstract: We prove a new characterization of the Ramsey property of categories in terms of a generalized form of K\H{o}nig's tree lemma. Afterwards, we discuss its applications to structural Ramsey theory. In particular, we provide a new proof of the existence and uniqueness of minimal Ramsey expansions and a new transfer theorem which uses Grothendieck opfibrations and unifies several known Ramsey transfers.

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Maximilian Hadek

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