Refinements of provability and consistency principles for the second incompleteness theorem
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916890945781760 |
|---|---|
| author | Kurahashi, Taishi |
| author_facet | Kurahashi, Taishi |
| contents | This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of the present paper, we show that the set $\{\mathbf{E},\mathbf{C}, \mathbf{D3}\}$ suffices to establish the unprovability of the consistency statement $\neg\, \mathrm{Pr}_T(\ulcorner 0=1 \urcorner)$. We also prove that the set $\{\mathbf{E}^{\mathrm{U}}, \mathbf{CB_{\exists}}\}$ yields formalized $Σ_1$-completeness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Refinements of provability and consistency principles for the second incompleteness theorem Kurahashi, Taishi Logic This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of the present paper, we show that the set $\{\mathbf{E},\mathbf{C}, \mathbf{D3}\}$ suffices to establish the unprovability of the consistency statement $\neg\, \mathrm{Pr}_T(\ulcorner 0=1 \urcorner)$. We also prove that the set $\{\mathbf{E}^{\mathrm{U}}, \mathbf{CB_{\exists}}\}$ yields formalized $Σ_1$-completeness. |
| title | Refinements of provability and consistency principles for the second incompleteness theorem |
| topic | Logic |
| url | https://arxiv.org/abs/2507.00955 |