The aim of this paper is to construct chains of length $(2^\kappa)^+$ in the sense of Rudin-Frol\'ik order in $\beta \kappa$ for $\kappa$ regular.
Ultrafilters without immediate predecessors in Rudin-Frolik order for regulars
The Rudin-Frolik order and the Ultrapower Axiom
A note on special subsets of the Rudin-Frolík order for regulars
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