Robinson Splitting Theorem and $Σ_1$ Induction
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910040879792128 |
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| author | Liu, Yong Peng, Cheng Sun, Mengzhou |
| author_facet | Liu, Yong Peng, Cheng Sun, Mengzhou |
| contents | The Robinson Splitting Theorem states that a c.e. degree $\mathbf{b}$ splits over any low c.e. degree $\mathbf{c}<\mathbf{b}$. We prove that a weaker version of this theorem holds in models of $\mathrm{P}^-+\mathrm{I}Σ_1$, with lowness replaced by superlowness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03994 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robinson Splitting Theorem and $Σ_1$ Induction Liu, Yong Peng, Cheng Sun, Mengzhou Logic 03F30, 03D25, 03H15 The Robinson Splitting Theorem states that a c.e. degree $\mathbf{b}$ splits over any low c.e. degree $\mathbf{c}<\mathbf{b}$. We prove that a weaker version of this theorem holds in models of $\mathrm{P}^-+\mathrm{I}Σ_1$, with lowness replaced by superlowness. |
| title | Robinson Splitting Theorem and $Σ_1$ Induction |
| topic | Logic 03F30, 03D25, 03H15 |
| url | https://arxiv.org/abs/2603.03994 |