A Note on a Theorem of Apter

Rahman Mohammadpour; Otto Rajala; Sebastiano Thei

A Note on a Theorem of Apter

Logic 2026-03-11 v1

Authors: Rahman Mohammadpour , Otto Rajala , Sebastiano Thei

Abstract

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

Keywords

set theory

Cite

@article{arxiv.2603.08915,
  title  = {A Note on a Theorem of Apter},
  author = {Rahman Mohammadpour and Otto Rajala and Sebastiano Thei},
  journal= {arXiv preprint arXiv:2603.08915},
  year   = {2026}
}

Comments

8 pages

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