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arXiv · 2505.22561

On Big Ramsey degrees of universal $ω$-edge-labeled hypergraphs

Jan Hubička·Matěj Konečný·Stevo Todorcevic·Andy Zucker
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Abstract

We show that the big Ramsey degrees of every countable universal $u$-uniform $ω$-edge-labeled hypergraph are infinite for every $u\geq 2$. Together with a recent result of Braunfeld, Chodounský, de Rancourt, Hubička, Kawach, and Konečný this finishes full characterisation of unrestricted relational structures with finite big Ramsey degrees.

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Jan Hubička, Matěj Konečný, Stevo Todorcevic, Andy Zucker. 2025-05-31. On Big Ramsey degrees of universal $ω$-edge-labeled hypergraphs. https://arxiv.org/abs/2505.22561

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