K\H{o}nig = Ramsey, A compactness lemma for Ramsey categories
Combinatorics
2025-08-18 v1
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.
Keywords
Cite
@article{arxiv.2508.11465,
title = {K\H{o}nig = Ramsey, A compactness lemma for Ramsey categories},
author = {Maximilian Hadek},
journal= {arXiv preprint arXiv:2508.11465},
year = {2025}
}
Comments
26 pages