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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.13049 |
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| _version_ | 1866914817434976256 |
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| author | Kurahashi, Taishi Visser, Albert |
| author_facet | Kurahashi, Taishi Visser, Albert |
| contents | In this paper, we study the employment of $Σ_1$-sentences with certificates, i.e., $Σ_1$-sentences where a number of principles is added to ensure that the witness is sufficiently number-like. We develop certificates in some detail and illustrate their use by reproving some classical results and proving some new ones. An example of such a classical result is Vaught's theorem of the strong effective inseparability of $\mathsf{R}_0$.
We also develop the new idea of a theory being ${\sf R}_{0{\sf p}}$-sourced. Using this notion, we can transfer a number of salient results from $\mathsf{R}_0$ to a variety of other theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13049 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Certified $Σ_1$-sentences Kurahashi, Taishi Visser, Albert Logic In this paper, we study the employment of $Σ_1$-sentences with certificates, i.e., $Σ_1$-sentences where a number of principles is added to ensure that the witness is sufficiently number-like. We develop certificates in some detail and illustrate their use by reproving some classical results and proving some new ones. An example of such a classical result is Vaught's theorem of the strong effective inseparability of $\mathsf{R}_0$. We also develop the new idea of a theory being ${\sf R}_{0{\sf p}}$-sourced. Using this notion, we can transfer a number of salient results from $\mathsf{R}_0$ to a variety of other theories. |
| title | Certified $Σ_1$-sentences |
| topic | Logic |
| url | https://arxiv.org/abs/2306.13049 |