Modal logical aspects of provability predicates and consistency statements
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908665644056576 |
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| author | Kogure, Haruka Kurahashi, Taishi |
| author_facet | Kogure, Haruka Kurahashi, Taishi |
| contents | This paper studies the modal logical aspects of provability predicates and consistency statements for theories of arithmetic. First, we provide an overview of previous works on the correspondence between various derivability conditions for provability predicates and different modal logics. The main technical contribution of the present paper is to establish the arithmetical completeness of the logics $\mathsf{NP}$, $\mathsf{ND}$, $\mathsf{NP4}$, and $\mathsf{ND4}$ by extending Solovay's method and refining Arai's construction of Rosser provability predicates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modal logical aspects of provability predicates and consistency statements Kogure, Haruka Kurahashi, Taishi Logic This paper studies the modal logical aspects of provability predicates and consistency statements for theories of arithmetic. First, we provide an overview of previous works on the correspondence between various derivability conditions for provability predicates and different modal logics. The main technical contribution of the present paper is to establish the arithmetical completeness of the logics $\mathsf{NP}$, $\mathsf{ND}$, $\mathsf{NP4}$, and $\mathsf{ND4}$ by extending Solovay's method and refining Arai's construction of Rosser provability predicates. |
| title | Modal logical aspects of provability predicates and consistency statements |
| topic | Logic |
| url | https://arxiv.org/abs/2511.15531 |