Big Ramsey Degrees and Infinite Languages
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913451042930688 |
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| author | Braunfeld, Samuel Chodounský, David de Rancourt, Noé Hubička, Jan Kawach, Jamal Konečný, Matěj |
| author_facet | Braunfeld, Samuel Chodounský, David de Rancourt, Noé Hubička, Jan Kawach, Jamal Konečný, Matěj |
| contents | This paper investigates big Ramsey degrees of unrestricted relational structures in (possibly) infinite languages. Despite significant progress in the study of big Ramsey degrees, the big Ramsey degrees of many classes of structures with finite small Ramsey degrees are still not well understood. We show that if there are only finitely many relations of every arity greater than one, then unrestricted relational structures have finite big Ramsey degrees, and give some evidence that this is tight. This is the first time finiteness of big Ramsey degrees has been established for a random structure in an infinite language. Our results represent an important step towards a better understanding of big Ramsey degrees for structures with relations of arity greater than two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_13116 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Big Ramsey Degrees and Infinite Languages Braunfeld, Samuel Chodounský, David de Rancourt, Noé Hubička, Jan Kawach, Jamal Konečný, Matěj Combinatorics Discrete Mathematics Logic 05D10, 05C05, 05C65, 05C55, 03C50, 03C55, 03E05, 03E15 This paper investigates big Ramsey degrees of unrestricted relational structures in (possibly) infinite languages. Despite significant progress in the study of big Ramsey degrees, the big Ramsey degrees of many classes of structures with finite small Ramsey degrees are still not well understood. We show that if there are only finitely many relations of every arity greater than one, then unrestricted relational structures have finite big Ramsey degrees, and give some evidence that this is tight. This is the first time finiteness of big Ramsey degrees has been established for a random structure in an infinite language. Our results represent an important step towards a better understanding of big Ramsey degrees for structures with relations of arity greater than two. |
| title | Big Ramsey Degrees and Infinite Languages |
| topic | Combinatorics Discrete Mathematics Logic 05D10, 05C05, 05C65, 05C55, 03C50, 03C55, 03E05, 03E15 |
| url | https://arxiv.org/abs/2301.13116 |