A Universe with a $Δ^1_n$-definable well-order of the reals, $\mathsf{CH}$ and $Π^1_n$-Uniformization
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913914819706880 |
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| author | Hoffelner, Stefan |
| author_facet | Hoffelner, Stefan |
| contents | This paper details the construction of a universe where $Π^1_3$-uniformization is true, the Continuum Hypothesis holds yet it possesses a $Δ^1_3$-definable well-order of its reals. The method can be lifted to canonical inner models with finitely many Woodin cardinals to produce universes of $\mathsf{CH}$, $Π^1_n$-uniformization and where additionally a $Δ^1_n$-definable well-order of the reals exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21778 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Universe with a $Δ^1_n$-definable well-order of the reals, $\mathsf{CH}$ and $Π^1_n$-Uniformization Hoffelner, Stefan Logic This paper details the construction of a universe where $Π^1_3$-uniformization is true, the Continuum Hypothesis holds yet it possesses a $Δ^1_3$-definable well-order of its reals. The method can be lifted to canonical inner models with finitely many Woodin cardinals to produce universes of $\mathsf{CH}$, $Π^1_n$-uniformization and where additionally a $Δ^1_n$-definable well-order of the reals exist. |
| title | A Universe with a $Δ^1_n$-definable well-order of the reals, $\mathsf{CH}$ and $Π^1_n$-Uniformization |
| topic | Logic |
| url | https://arxiv.org/abs/2506.21778 |