@article {Shimura:July 2000:0039-3215:237, author = "Shimura T.", title = "Kripke Incompleteness of Predicate Extensions of the Modal Logics Axiomatized by a Canonical Formula for a Frame with a Nontrivial Cluster", journal = "Studia Logica", volume = "65", year = "July 2000", abstract = "
We generalize the incompleteness proof of the modal predicate logic Q-S4+ 
p

p + BF described in Hughes-Cresswell [6]. As a corollary, we show that, for every subframe logic Lcontaining S4, Kripke completeness of Q-L+ BF implies the finite embedding property of L.