On $\omega$-strongly measurable cardinals in $\mathbb{P}_{\max}$ extensions

Navin Aksornthong; Takehiko Gappo; James Holland; Grigor Sargsyan

On $\omega$-strongly measurable cardinals in $\mathbb{P}_{\max}$ extensions

Logic 2025-07-01 v2

Authors: Navin Aksornthong , Takehiko Gappo , James Holland , Grigor Sargsyan

Abstract

We show that in the $\mathbb{P}_{\max}$ extension of a certain Chang-type model of determinacy, if $\kappa\in\{\omega_1, \omega_2, \omega_3\}$ , then the restriction of the club filter on $\kappa\cap\mathrm{Cof}(\omega)$ to HOD is an ultrafilter in HOD. This answers Question 4.11 of [BNH23] raised by Ben-Neria and Hayut.

Keywords

omega-strongly measurable cardinals P_max extension Chang-type model club filter HOD ultrafilter

Cite

@article{arxiv.2307.13682,
  title  = {On $\omega$-strongly measurable cardinals in $\mathbb{P}_{\max}$ extensions},
  author = {Navin Aksornthong and Takehiko Gappo and James Holland and Grigor Sargsyan},
  journal= {arXiv preprint arXiv:2307.13682},
  year   = {2025}
}

Comments

22 pages. arXiv admin note: text overlap with arXiv:2307.08607

On $\omega$-strongly measurable cardinals in $\mathbb{P}_{\max}$ extensions

Abstract

Keywords

Cite

Comments

Related papers