The adjacent Hindman's theorem and the $\mathbb Z$-Ramsey's theorem
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910030556561408 |
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| author | Aceves-Martínez, Bruno Fernando Fernández-Bretón, David J. Romero-García, L. F. Villagómez-Canela, Luis F. |
| author_facet | Aceves-Martínez, Bruno Fernando Fernández-Bretón, David J. Romero-García, L. F. Villagómez-Canela, Luis F. |
| contents | We consider the restriction of Ramsey's theorem that arises from considering only translation-invariant colourings of pairs, and show that this has the same strength (both from the viewpoint of Reverse Mathematics and from the viewpoint of Computability Theory) as the {\em Adjacent Hindman's Theorem}, proposed by L. Carlucci (Arch. Math. Log. {\bf 57} (2018), 381--359). We also investigate some higher dimensional versions of both of these statements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14558 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The adjacent Hindman's theorem and the $\mathbb Z$-Ramsey's theorem Aceves-Martínez, Bruno Fernando Fernández-Bretón, David J. Romero-García, L. F. Villagómez-Canela, Luis F. Logic Combinatorics Primary 03F35, 03D30, Secondary 05D10 We consider the restriction of Ramsey's theorem that arises from considering only translation-invariant colourings of pairs, and show that this has the same strength (both from the viewpoint of Reverse Mathematics and from the viewpoint of Computability Theory) as the {\em Adjacent Hindman's Theorem}, proposed by L. Carlucci (Arch. Math. Log. {\bf 57} (2018), 381--359). We also investigate some higher dimensional versions of both of these statements. |
| title | The adjacent Hindman's theorem and the $\mathbb Z$-Ramsey's theorem |
| topic | Logic Combinatorics Primary 03F35, 03D30, Secondary 05D10 |
| url | https://arxiv.org/abs/2412.14558 |