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

Navin Aksornthong, Takehiko Gappo, James Holland +1

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 $κ\cap\mathrm…