On Big Ramsey degrees of universal $ω$-edge-labeled hypergraphs
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915523520888832 |
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| author | Hubička, Jan Konečný, Matěj Todorcevic, Stevo Zucker, Andy |
| author_facet | Hubička, Jan Konečný, Matěj Todorcevic, Stevo Zucker, Andy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22561 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Big Ramsey degrees of universal $ω$-edge-labeled hypergraphs Hubička, Jan Konečný, Matěj Todorcevic, Stevo Zucker, Andy Combinatorics Discrete Mathematics Logic 05C55, 03E02, 05D10, 05C15 G.2.1 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. |
| title | On Big Ramsey degrees of universal $ω$-edge-labeled hypergraphs |
| topic | Combinatorics Discrete Mathematics Logic 05C55, 03E02, 05D10, 05C15 G.2.1 |
| url | https://arxiv.org/abs/2505.22561 |