Characterisation of the big Ramsey degrees of the generic partial order
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916980644118528 |
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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 | As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite partial orders endowed with linear extensions form a Ramsey class (this result was announced by Nešetřil and Rödl in 1984 with first published proof by Paoli, Trotter and Walker in 1985). Towards this, we refine earlier upper bounds obtained by Hubička based on a new connection of big Ramsey degrees to the Carlson-Simpson theorem and we also introduce a new technique of giving lower bounds using an iterated application of the upper-bound theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10088 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterisation of the big Ramsey degrees of the generic partial order Balko, Martin Chodounský, David Dobrinen, Natasha Hubička, Jan Konečný, Matěj Vena, Lluis Zucker, Andy Combinatorics Discrete Mathematics Logic 05D10, 05C05, 05C65, 05C55, 06A07 G.2.2; F.4.1 As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite partial orders endowed with linear extensions form a Ramsey class (this result was announced by Nešetřil and Rödl in 1984 with first published proof by Paoli, Trotter and Walker in 1985). Towards this, we refine earlier upper bounds obtained by Hubička based on a new connection of big Ramsey degrees to the Carlson-Simpson theorem and we also introduce a new technique of giving lower bounds using an iterated application of the upper-bound theorem. |
| title | Characterisation of the big Ramsey degrees of the generic partial order |
| topic | Combinatorics Discrete Mathematics Logic 05D10, 05C05, 05C65, 05C55, 06A07 G.2.2; F.4.1 |
| url | https://arxiv.org/abs/2303.10088 |