Pretabular varieties of modal algebras

Studia Logica 39 (2-3):101 - 124 (1980)
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Abstract

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras.

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Citations of this work

The structure of lattices of subframe logics.Frank Wolter - 1997 - Annals of Pure and Applied Logic 86 (1):47-100.
Algebraic semantics for quasi-classical modal logics.W. J. Blok & P. Köhler - 1983 - Journal of Symbolic Logic 48 (4):941-964.
Hereditarily structurally complete modal logics.V. V. Rybakov - 1995 - Journal of Symbolic Logic 60 (1):266-288.

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References found in this work

Some embedding theorems for modal logic.David Makinson - 1971 - Notre Dame Journal of Formal Logic 12 (2):252-254.
Five critical modal systems.L. Esakia & V. Meskhi - 1977 - Theoria 43 (1):52-60.

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