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arXiv · 2508.11465

Kőnig = Ramsey, A compactness lemma for Ramsey categories

Maximilian Hadek
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Abstract

We prove a new characterization of the Ramsey property of categories in terms of a generalized form of Kőnig'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. 2025-08-15. Kőnig = Ramsey, A compactness lemma for Ramsey categories. https://arxiv.org/abs/2508.11465

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