More rigid ideals

Abstract

We extend prior results of Cody-Eskew, showing the consistency of GCH with the statement that for all regular cardinals $\kappa \le \lambda$, where $\kappa$ is the successor of a regular cardinal, there is a rigid saturated ideal on ${\mathcal{P}}_{\kappa }\lambda$. We also show the consistency of some instances of rigid saturated ideals on ${\mathcal{P}}_{\kappa }\lambda$ where $\kappa$ is the successor of a singular cardinal.