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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.14821 |
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| _version_ | 1866909852006088704 |
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| author | Holy, Peter Schilhan, Jonathan |
| author_facet | Holy, Peter Schilhan, Jonathan |
| contents | We provide, for any regular uncountable cardinal $κ$, a new argument for Pincus' result on the consistency of $\mathrm{ZF}$ with the higher dependent choice principle $\mathrm{DC}_{<κ}$ and the ordering principle in the presence of a failure of the axiom of choice. We also generalise his methods and obtain these consistency results in a larger class of models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Ordering Principle and Higher Dependent Choice Holy, Peter Schilhan, Jonathan Logic 03E25, 03E35, 06A05 We provide, for any regular uncountable cardinal $κ$, a new argument for Pincus' result on the consistency of $\mathrm{ZF}$ with the higher dependent choice principle $\mathrm{DC}_{<κ}$ and the ordering principle in the presence of a failure of the axiom of choice. We also generalise his methods and obtain these consistency results in a larger class of models. |
| title | The Ordering Principle and Higher Dependent Choice |
| topic | Logic 03E25, 03E35, 06A05 |
| url | https://arxiv.org/abs/2510.14821 |