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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Kit Fine (1971). The Logics Containing S 4.3. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):371-376.

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