Ultrafilters without immediate predecessors in Rudin-Frolik order for regulars

Abstract

The aim of this paper is to construct ultrafilters without immediate predecessors in the Rudin-Frolik order in $\beta \kappa \setminus \kappa$, where $\kappa$ is a regular cardinal. This generalizes the problem posed by Peter Simon more than 40 years ago.

arXiv admin note: substantial text overlap with arXiv:2304.02143, arXiv:2304.00097, arXiv:2304.01398