Power $Σ_1$ in Card with two Woodin cardinals
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908879651078144 |
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| author | Schlutzenberg, Farmer |
| author_facet | Schlutzenberg, Farmer |
| contents | Väänänen and Welch asked in the paper "When cardinals determine the power set: inner models and Härtig quantifier logic" which large cardinals are consistent with the power set operation $x\mapsto P(x)$ being $Σ_1$-definable in the predicate Card of all cardinals. We show that, relative to large cardinals, this property is consistent together with the existence of two Woodin cardinals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05243 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power $Σ_1$ in Card with two Woodin cardinals Schlutzenberg, Farmer Logic 03E45, 03E55 Väänänen and Welch asked in the paper "When cardinals determine the power set: inner models and Härtig quantifier logic" which large cardinals are consistent with the power set operation $x\mapsto P(x)$ being $Σ_1$-definable in the predicate Card of all cardinals. We show that, relative to large cardinals, this property is consistent together with the existence of two Woodin cardinals. |
| title | Power $Σ_1$ in Card with two Woodin cardinals |
| topic | Logic 03E45, 03E55 |
| url | https://arxiv.org/abs/2505.05243 |