Abstract

We study the variety of Löb algebras, the algebraic structures associated with Formal Propositional Calculus. Among other things, we show that there exist only two maximal intermediate logics in the lattice of intermediate logics over Basic Propositional Calculus. We introduce countably many locally finite sub-varieties of the variety of Löb algebras and show that their corresponding intermediate logics have the interpolation property. Finally, we characterize all chain basic algebras with empty set of generators, and show that there are continuum many such chain basic algebras