Varieties of positive modal algebras and structural completeness

Review of Symbolic Logic 12 (3):557-588 (2019)
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Abstract

Positive modal algebras are the$$\left\langle { \wedge, \vee,\diamondsuit,\square,0,1} \right\rangle $$-subreducts of modal algebras. We prove that the variety of positive S4-algebras is not locally finite. On the other hand, the free one-generated positive S4-algebra is shown to be finite. Moreover, we describe the bottom part of the lattice of varieties of positive S4-algebras. Building on this, we characterize structurally complete varieties of positive K4-algebras.

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