Bounded Ramsey's theorem for triples in computability theory
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910097616142336 |
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| author | Patey, Ludovic Shafer, Paul |
| author_facet | Patey, Ludovic Shafer, Paul |
| contents | We study a restriction of Ramsey's theorem for 2-coloring of triples, in which homogeneous sets for color~1 are of bounded size ($\mathsf{BRT}^3_2$). We prove that the computational content of this statement is very close to Ramsey's theorem for pairs ($\mathsf{RT}^2_2)$, in that it satisfies the same known computability-theoretic upper bounds, but that $\mathsf{BRT}^3_2$ is not computably-reducible to $\mathsf{RT}^2_2$, even when allowing multiple applications of $\mathsf{RT}^2_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02092 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bounded Ramsey's theorem for triples in computability theory Patey, Ludovic Shafer, Paul Logic 03B30 03D80 05D10 We study a restriction of Ramsey's theorem for 2-coloring of triples, in which homogeneous sets for color~1 are of bounded size ($\mathsf{BRT}^3_2$). We prove that the computational content of this statement is very close to Ramsey's theorem for pairs ($\mathsf{RT}^2_2)$, in that it satisfies the same known computability-theoretic upper bounds, but that $\mathsf{BRT}^3_2$ is not computably-reducible to $\mathsf{RT}^2_2$, even when allowing multiple applications of $\mathsf{RT}^2_2$. |
| title | Bounded Ramsey's theorem for triples in computability theory |
| topic | Logic 03B30 03D80 05D10 |
| url | https://arxiv.org/abs/2604.02092 |