On a Theorem by Bezboruah & Shepherdson
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917460101300224 |
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| author | Visser, Albert |
| author_facet | Visser, Albert |
| contents | We discuss an incompleteness result proven by Bezboruah and Shepherdson. This result tells us that the weak theory ${\sf PA}^-$ does not prove the consistency of any theory (under certain assumptions explained in the paper). Kreisel argued that such a result is not meaningful. We discuss Kreisel's objection and conclude that his argument does not hold water. We compare Pudlák's extension of the Second Incompleteness Theorem with the Bezboruah-Sheperdson Theorem. Finally, we reprove the Bezboruah-Sheperdson Theorem for a sequence coding based on an insight of Nielsen and Markov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a Theorem by Bezboruah & Shepherdson Visser, Albert Logic 03A05, 03F25, 03F40 We discuss an incompleteness result proven by Bezboruah and Shepherdson. This result tells us that the weak theory ${\sf PA}^-$ does not prove the consistency of any theory (under certain assumptions explained in the paper). Kreisel argued that such a result is not meaningful. We discuss Kreisel's objection and conclude that his argument does not hold water. We compare Pudlák's extension of the Second Incompleteness Theorem with the Bezboruah-Sheperdson Theorem. Finally, we reprove the Bezboruah-Sheperdson Theorem for a sequence coding based on an insight of Nielsen and Markov. |
| title | On a Theorem by Bezboruah & Shepherdson |
| topic | Logic 03A05, 03F25, 03F40 |
| url | https://arxiv.org/abs/2603.06068 |