The Axiom of Choice in the $κ$-Mantle
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914714170163200 |
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| author | Lietz, Andreas |
| author_facet | Lietz, Andreas |
| contents | Usuba has asked whether the $κ$-mantle, the intersection of all grounds that extend to $V$ via a forcing of size ${<}κ$, is always a model of ZFC. We give a negative answers by constructing counterexamples where $κ$ is a Mahlo cardinal, $κ=ω_1$ and where $κ$ is the successor of a regular uncountable cardinal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Axiom of Choice in the $κ$-Mantle Lietz, Andreas Logic 03E25 03E35 03E55 Usuba has asked whether the $κ$-mantle, the intersection of all grounds that extend to $V$ via a forcing of size ${<}κ$, is always a model of ZFC. We give a negative answers by constructing counterexamples where $κ$ is a Mahlo cardinal, $κ=ω_1$ and where $κ$ is the successor of a regular uncountable cardinal. |
| title | The Axiom of Choice in the $κ$-Mantle |
| topic | Logic 03E25 03E35 03E55 |
| url | https://arxiv.org/abs/2403.09015 |