On $\ddot{I}‰$-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 $\hat{I}º\in \{\ddot{I}{‰}_1,\ddot{I}{‰}_2,\ddot{I}{‰}_3\}$, then the restriction of the club filter on $κ\cap\m…