Conservation of Ramsey's theorem for pairs and well-foundedness
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917762088042496 |
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| author | Houérou, Quentin Le Patey, Ludovic Levy Yokoyama, Keita |
| author_facet | Houérou, Quentin Le Patey, Ludovic Levy Yokoyama, Keita |
| contents | In this article, we prove that Ramsey's theorem for pairs and two colors is $Π^1_1$-conservative over~$\mathsf{RCA}_0 + \mathsf{B}Σ^0_2 + \mathsf{WF}(ε_0)$ and over~$\mathsf{RCA}_0 + \mathsf{B}Σ^0_2 + \bigcup_n \mathsf{WF}(ω^ω_n)$. These results improve theorems from Chong, Slaman and Yang and Kołodziejczyk and Yokoyama and belong to a long line of research towards the characterization of the first-order part of Ramsey's theorem for pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11616 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conservation of Ramsey's theorem for pairs and well-foundedness Houérou, Quentin Le Patey, Ludovic Levy Yokoyama, Keita Logic In this article, we prove that Ramsey's theorem for pairs and two colors is $Π^1_1$-conservative over~$\mathsf{RCA}_0 + \mathsf{B}Σ^0_2 + \mathsf{WF}(ε_0)$ and over~$\mathsf{RCA}_0 + \mathsf{B}Σ^0_2 + \bigcup_n \mathsf{WF}(ω^ω_n)$. These results improve theorems from Chong, Slaman and Yang and Kołodziejczyk and Yokoyama and belong to a long line of research towards the characterization of the first-order part of Ramsey's theorem for pairs. |
| title | Conservation of Ramsey's theorem for pairs and well-foundedness |
| topic | Logic |
| url | https://arxiv.org/abs/2402.11616 |