Total Failure of Approachability at Successors of Singulars of Countable Cofinality

Hannes Jakob

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arXiv · 2508.02867

Total Failure of Approachability at Successors of Singulars of Countable Cofinality

Hannes Jakob

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Abstract

Relative to class many supercompact cardinals, we construct a model of $\ZFC+\GCH$ where for every singular cardinal $\delta$ of countable cofinality and every regular uncountable $\mu<\delta$ there are stationarily many non-approachable points of cofinality $\mu$ in $\delta^+$. This answers a question of Mitchell and provides a decisive answer to a question of Foreman and Shelah.

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BibTeX RIS

Hannes Jakob. 2025-08-04. Total Failure of Approachability at Successors of Singulars of Countable Cofinality. https://arxiv.org/abs/2508.02867

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