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VARIETIES OF POSITIVE MODAL ALGEBRAS AND STRUCTURAL COMPLETENESS
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- Journal:
- The Review of Symbolic Logic / Volume 12 / Issue 3 / September 2019
- Published online by Cambridge University Press:
- 13 June 2019, pp. 557-588
- Print publication:
- September 2019
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- Article
- Export citation
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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 (passively, hereditarily) structurally complete varieties of positive K4-algebras.
