Forcing the $Π^1_3$-Reduction Property and a Failure of $Π^1_3$-Uniformization
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866914470158139392 |
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| author | Hoffelner, Stefan |
| author_facet | Hoffelner, Stefan |
| contents | We force over the constructible universe to obtain a model of the $Π^1_3$-reduction property, thus lowering the best known large cardinal strength from the existence of $M_1^{\#}$ to just ZFC. In this model the $Π^1_3$-uniformization property fails, which separates these two principles for the first time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_02209 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Forcing the $Π^1_3$-Reduction Property and a Failure of $Π^1_3$-Uniformization Hoffelner, Stefan Logic 03E15, 03E35, 03E45 We force over the constructible universe to obtain a model of the $Π^1_3$-reduction property, thus lowering the best known large cardinal strength from the existence of $M_1^{\#}$ to just ZFC. In this model the $Π^1_3$-uniformization property fails, which separates these two principles for the first time. |
| title | Forcing the $Π^1_3$-Reduction Property and a Failure of $Π^1_3$-Uniformization |
| topic | Logic 03E15, 03E35, 03E45 |
| url | https://arxiv.org/abs/2009.02209 |