VARIETIES OF POSITIVE MODAL ALGEBRAS AND STRUCTURAL COMPLETENESS
Tommaso Moraschini · The Review of Symbolic Logic · 2019
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 (passively, hereditarily) structurally complete varieties of positive K4-algebras.