On $\boldsymbolΣ^1_3$- and $Σ^1_4$-uniformization
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914494811209728 |
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| author | Hoffelner, Stefan |
| author_facet | Hoffelner, Stefan |
| contents | Assuming the consistency of $\mathsf{ZFC}$, we construct a model of set theory in which the boldface $\mathbfΣ^1_3$-uniformization property holds, yet the lightface $Σ^1_4$-uniformization property fails, separating these two principles for the first time. We also indicate how to create a universe where $Σ^1_3$-uniformization holds, but $Σ^1_4$-uniformization fails using inner models with large cardinals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19360 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On $\boldsymbolΣ^1_3$- and $Σ^1_4$-uniformization Hoffelner, Stefan Logic 03E35, 03E45, 03E15, 03E55, 03E57 Assuming the consistency of $\mathsf{ZFC}$, we construct a model of set theory in which the boldface $\mathbfΣ^1_3$-uniformization property holds, yet the lightface $Σ^1_4$-uniformization property fails, separating these two principles for the first time. We also indicate how to create a universe where $Σ^1_3$-uniformization holds, but $Σ^1_4$-uniformization fails using inner models with large cardinals. |
| title | On $\boldsymbolΣ^1_3$- and $Σ^1_4$-uniformization |
| topic | Logic 03E35, 03E45, 03E15, 03E55, 03E57 |
| url | https://arxiv.org/abs/2604.19360 |