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arXiv · 2307.13682

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

Navin Aksornthong·Takehiko Gappo·James Holland·Grigor Sargsyan
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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.

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Navin Aksornthong, Takehiko Gappo, James Holland, Grigor Sargsyan. 2023-07-25. On $\omega$-strongly measurable cardinals in $\mathbb{P}_{\max}$ extensions. https://arxiv.org/abs/2307.13682

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