A Note on a Theorem of Apter

Abstract

We show that the consistency of $\mathrm{ZF}+{\mathrm{AD}}_{\mathbb{R}}+‘‘\hat{I}˜$ is measurable$"$ implies the consistency of $\mathrm{ZF}+‘‘\hat{I}˜$ is the least strongly regular cardinal and the least measurable cardinal$"$ + $‘‘$all uncountable cardinals below $\hat{I}˜$ are of countable cofinality$"$.

8 pages