Our investigation is concerned with the finite model property (fmp) with respect to admissible rules. We establish general sufficient conditions for absence of frnp w. I. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic X containing K4 with the co-cover property and of width > 2 has fmp w. I. t . admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem -K4 itself, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp -the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width 5 2, there exists a zone for fmp w. r. t. admissibility. It is shown (Theorem 4.3) that all modal logics X of width 5 2 extending S4 which are not sub-logics of three special tabular logics (which is equipotent to all these X extend a certain subframe logic defined over S4 by omission of four special frames) have fmp w. I. t. admissibility.Mathematics Subject Classification: 03B45, 03F07.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.