Total Failure of Approachability at Successors of Singulars of Countable Cofinality
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.
Publication Details
- Journal
- arXiv (Cornell University)
- Published
- 2025-08-04
- Primary Topic
- Advanced Topology and Set Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00