On Big Ramsey degrees of universal $\omega$-edge-labeled hypergraphs

Jan Hubička; Matěj Konečný; Stevo Todorcevic; Andy Zucker

On Big Ramsey degrees of universal $\omega$-edge-labeled hypergraphs

Combinatorics 2025-10-01 v2 Discrete Mathematics Logic

Authors: Jan Hubička , Matěj Konečný , Stevo Todorcevic , Andy Zucker

Abstract

We show that the big Ramsey degrees of every countable universal $u$ -uniform $\omega$ -edge-labeled hypergraph are infinite for every $u\geq 2$ . Together with a recent result of Braunfeld, Chodounsk\'y, de Rancourt, Hubi\v{c}ka, Kawach, and Kone\v{c}n\'y this finishes full characterisation of unrestricted relational structures with finite big Ramsey degrees.

Keywords

big Ramsey degrees universal hypergraph $\omega$-edge-labeled relational structures Ramsey theory

Cite

@article{arxiv.2505.22561,
  title  = {On Big Ramsey degrees of universal $\omega$-edge-labeled hypergraphs},
  author = {Jan Hubička and Matěj Konečný and Stevo Todorcevic and Andy Zucker},
  journal= {arXiv preprint arXiv:2505.22561},
  year   = {2025}
}

Comments

6 pages, 1 figure, accepted to Eurocomb 2025. Minor revision with updated citations and introduction

On Big Ramsey degrees of universal $\omega$-edge-labeled hypergraphs

Abstract

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