On Strong Neighbourhood Completeness of
Modal and Intermediate Propositional Logic
(Part II)

Valentin Shehtman

Institute of Information Transmission Problems
Russian Academy of Sciences
B. Karetny 19
101447 Moscow
RUSSIA
shehtman@lpcs.math.msu.ru

Abstract

The property of strong neighbourhood completeness was introduced in the first part of this paper. By modifying the ultrabouqet construction, we prove this property for all Kripke-complete normal K4-logics and for a large class of Kripke-complete polymodal logics (called `acyclic'). On the other hand, we present a simple counterexample of a polymodal logic with the f.m.p. which is not strongly neighbourhood complete.

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