The finite cohesiveness principle
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908833919533056 |
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| author | Sun, Mengzhou |
| author_facet | Sun, Mengzhou |
| contents | We investigate the logical strength of the cohesiveness principle when restricted to finite sequences of sets, denoted by fin-COH, over different base theories. Our main result shows that fin-COH entails $IΣ_1^0$ over the weaker base theory $RCA_0^*$, thereby answering a question posed by Fiori-Carones, Kołodziejczyk and Kowalik. In addition, we show that fin-COH is not provable over $WKL_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18383 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The finite cohesiveness principle Sun, Mengzhou Logic 03B30, 03C62, 03F35, 03F30, 05D10 We investigate the logical strength of the cohesiveness principle when restricted to finite sequences of sets, denoted by fin-COH, over different base theories. Our main result shows that fin-COH entails $IΣ_1^0$ over the weaker base theory $RCA_0^*$, thereby answering a question posed by Fiori-Carones, Kołodziejczyk and Kowalik. In addition, we show that fin-COH is not provable over $WKL_0$. |
| title | The finite cohesiveness principle |
| topic | Logic 03B30, 03C62, 03F35, 03F30, 05D10 |
| url | https://arxiv.org/abs/2503.18383 |