On the existence of skinny stationary subsets

Abstract

Matsubara–Usuba [13] introduced the notion of skinniness and its variants for subsets of ${\mathcal{P}}_{\kappa }\lambda$ and showed that the existence of skinny stationary subsets of ${\mathcal{P}}_{\kappa }\lambda$ is related to large cardinal properties of ideals over ${\mathcal{P}}_{\kappa }\lambda$ and to Jensen's diamond principle on λ. In this paper, we study the existence of skinny stationary sets in more detail.