Studia Logica 49 (4):455 - 470 (1990)

Abstract
Given a normal (multi-)modal logic a characterization is given of the finitely presentable algebras A whose logics L A split the lattice of normal extensions of . This is a substantial generalization of Rautenberg [10] and [11] in which is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by Blok [2] that for all cycle-free and finite A L A splits the lattice of normal extensions of K. Although we firmly believe it to be true, we have not been able to prove that if a logic splits the lattice of extensions of then is the logic of an algebra finitely presentable over ; in this respect our result remains partial.
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DOI 10.1007/BF00370158
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References found in this work BETA

An Ascending Chain of S4 Logics.Kit Fine - 1974 - Theoria 40 (2):110-116.
Logics Containing K4. Part I.Kit Fine - 1974 - Journal of Symbolic Logic 39 (1):31-42.
The Lattice of Modal Logics: An Algebraic Investigation.W. J. Blok - 1980 - Journal of Symbolic Logic 45 (2):221-236.
Splitting Lattices of Logics.Wolfgang Rautenberg - 1980 - Archive for Mathematical Logic 20 (3-4):155-159.
On the Degree of Incompleteness of Modal Logics.W. Blok - 1978 - Bulletin of the Section of Logic 7 (4):167-172.

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Citations of this work BETA

Shifting Priorities: Simple Representations for Twenty-Seven Iterated Theory Change Operators.Hans Rott - 2006 - In David Makinson, Jacek Malinowski & Heinrich Wansing (eds.), Towards Mathematical Philosophy. Dordrecht: Springer. pp. 269–296.
Canonical Formulas for K4. Part I: Basic Results.Michael Zakharyaschev - 1992 - Journal of Symbolic Logic 57 (4):1377-1402.
Canonical Rules.Emil Jeřábek - 2009 - Journal of Symbolic Logic 74 (4):1171 - 1205.
The Structure of Lattices of Subframe Logics.Frank Wolter - 1997 - Annals of Pure and Applied Logic 86 (1):47-100.
Splittings and the Finite Model Property.Marcus Kracht - 1993 - Journal of Symbolic Logic 58 (1):139-157.

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