On the Kunen–Shelah properties in Banach spaces

Abstract

We introduce and study the Kunen&#8211;Shelah properties ${\rm KS}_i$, $ i=0,1,\ldots ,7$. Let us highlight some of our results for a Banach space $X$: (1)&nbsp;$X^*$ has a $w^*$-nonseparable equivalent dual ball iff $X$ has an $\omega$-<i>polyhedron</