On hereditary normality of $\omega ^*$, Kunen points and character $\omega_{1}$

Abstract

We show that $\omega ^{*}\setminus \{p\}$ is not normal, if $p$ is a limit point of some countable subset of $\omega ^{*}$, consisting of points of character $\omega _{1}$. Moreover, such a point $p$ is a Kunen point and a super Kunen point.