Total Failure of Approachability at Successors of Singulars of Countable Cofinality
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914502981713920 |
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| author | Jakob, Hannes |
| author_facet | Jakob, Hannes |
| contents | Relative to class many supercompact cardinals, we construct a model of $\ZFC+\GCH$ where for every singular cardinal $δ$ of countable cofinality and every regular uncountable $μ<δ$ there are stationarily many non-approachable points of cofinality $μ$ in $δ^+$. This answers a question of Mitchell and provides a decisive answer to a question of Foreman and Shelah. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02867 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Total Failure of Approachability at Successors of Singulars of Countable Cofinality Jakob, Hannes Logic 03E05, 03E35, 03E55 Relative to class many supercompact cardinals, we construct a model of $\ZFC+\GCH$ where for every singular cardinal $δ$ of countable cofinality and every regular uncountable $μ<δ$ there are stationarily many non-approachable points of cofinality $μ$ in $δ^+$. This answers a question of Mitchell and provides a decisive answer to a question of Foreman and Shelah. |
| title | Total Failure of Approachability at Successors of Singulars of Countable Cofinality |
| topic | Logic 03E05, 03E35, 03E55 |
| url | https://arxiv.org/abs/2508.02867 |