Relative leftmost path principles and omega-model reflections of transfinite inductions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909644487655424 |
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| author | Suzuki, Yudai |
| author_facet | Suzuki, Yudai |
| contents | In this paper, we give characterizations of Towsner's relative leftmost path principles in terms of omega-model reflections of transfinite inductions. In particular, we show that the omega-model reflection of $Π^1_{n+1}$ transfinite induction is equivalent to the $Σ^0_n$ relative leftmost path principle over $\mathsf{RCA}_0$ for $n > 1$. As a consequence, we have that $Σ^0_{n+1}\mathsf{LPP}$ is strictly stronger than $Σ^0_{n}\mathsf{LPP}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_13504 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative leftmost path principles and omega-model reflections of transfinite inductions Suzuki, Yudai Logic In this paper, we give characterizations of Towsner's relative leftmost path principles in terms of omega-model reflections of transfinite inductions. In particular, we show that the omega-model reflection of $Π^1_{n+1}$ transfinite induction is equivalent to the $Σ^0_n$ relative leftmost path principle over $\mathsf{RCA}_0$ for $n > 1$. As a consequence, we have that $Σ^0_{n+1}\mathsf{LPP}$ is strictly stronger than $Σ^0_{n}\mathsf{LPP}$. |
| title | Relative leftmost path principles and omega-model reflections of transfinite inductions |
| topic | Logic |
| url | https://arxiv.org/abs/2407.13504 |