A Failure of $Π^1_{n+3}$-Reduction in the Presence of $Σ^1_{n+3}$-Separation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910126448836608 |
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| author | Hoffelner, Stefan |
| author_facet | Hoffelner, Stefan |
| contents | We show that one can force over $L$ that $Σ^1_3$-separation holds, while $Π^1_3$-reduction fails, thus separating these two principles for the first time. The construction can be lifted to canonical inner models $M_n$ with $n$-many Woodin cardinals, yielding that assuming the existence of $M_n$, $Σ^1_{n+3}$-separation can hold, yet $Π^1_{n+3}$-reduction fails. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02540 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Failure of $Π^1_{n+3}$-Reduction in the Presence of $Σ^1_{n+3}$-Separation Hoffelner, Stefan Logic 03E15, 03E35, 03E45 We show that one can force over $L$ that $Σ^1_3$-separation holds, while $Π^1_3$-reduction fails, thus separating these two principles for the first time. The construction can be lifted to canonical inner models $M_n$ with $n$-many Woodin cardinals, yielding that assuming the existence of $M_n$, $Σ^1_{n+3}$-separation can hold, yet $Π^1_{n+3}$-reduction fails. |
| title | A Failure of $Π^1_{n+3}$-Reduction in the Presence of $Σ^1_{n+3}$-Separation |
| topic | Logic 03E15, 03E35, 03E45 |
| url | https://arxiv.org/abs/2312.02540 |