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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2409.05973 |
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| _version_ | 1866912852851294208 |
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| author | Towsner, Henry Walsh, James |
| author_facet | Towsner, Henry Walsh, James |
| contents | For which choices of $X,Y,Z\in\{Σ^1_1,Π^1_1\}$ does no sufficiently strong $X$-sound and $Y$-definable extension theory prove its own $Z$-soundness? We give a complete answer, thereby delimiting the generalizations of Gödel's second incompleteness theorem that hold within second-order arithmetic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05973 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A classification of incompleteness statements Towsner, Henry Walsh, James Logic For which choices of $X,Y,Z\in\{Σ^1_1,Π^1_1\}$ does no sufficiently strong $X$-sound and $Y$-definable extension theory prove its own $Z$-soundness? We give a complete answer, thereby delimiting the generalizations of Gödel's second incompleteness theorem that hold within second-order arithmetic. |
| title | A classification of incompleteness statements |
| topic | Logic |
| url | https://arxiv.org/abs/2409.05973 |