Hereditarily structurally complete modal logics

Journal of Symbolic Logic 60 (1):266-288 (1995)
We consider structural completeness in modal logics. The main result is the necessary and sufficient condition for modal logics over K4 to be hereditarily structurally complete: a modal logic λ is hereditarily structurally complete $\operatorname{iff} \lambda$ is not included in any logic from the list of twenty special tabular logics. Hence there are exactly twenty maximal structurally incomplete modal logics above K4 and they are all tabular
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DOI 10.2307/2275521
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The Logics Containing S 4.3.Kit Fine - 1971 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):371-376.
Pretabular Varieties of Modal Algebras.W. J. Blok - 1980 - Studia Logica 39 (2-3):101 - 124.

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Linear Temporal Logic with Until and Next, Logical Consecutions.V. Rybakov - 2008 - Annals of Pure and Applied Logic 155 (1):32-45.

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