Exact big Ramsey degrees for finitely constrained binary free amalgamation classes
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866918046801592320 |
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| author | Balko, Martin Chodounský, David Dobrinen, Natasha Hubička, Jan Konečný, Matěj Vena, Lluis Zucker, Andy |
| author_facet | Balko, Martin Chodounský, David Dobrinen, Natasha Hubička, Jan Konečný, Matěj Vena, Lluis Zucker, Andy |
| contents | We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization, we show that the Fraïssé limit of each such class admits a strong big Ramsey structure, implying that the automorphism group of the Fraïssé limit has a metrizable universal completion flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_08409 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Exact big Ramsey degrees for finitely constrained binary free amalgamation classes Balko, Martin Chodounský, David Dobrinen, Natasha Hubička, Jan Konečný, Matěj Vena, Lluis Zucker, Andy Logic Combinatorics We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization, we show that the Fraïssé limit of each such class admits a strong big Ramsey structure, implying that the automorphism group of the Fraïssé limit has a metrizable universal completion flow. |
| title | Exact big Ramsey degrees for finitely constrained binary free amalgamation classes |
| topic | Logic Combinatorics |
| url | https://arxiv.org/abs/2110.08409 |