Total Failure of Approachability at Successors of Singulars of Countable Cofinality

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.

35 pages, accepted to Advances in Mathematics