On Lob algebras

摘要

We study the variety of Lob algebras , the algebraic structures associated with formal propositional calculus. Among other things, we prove a completeness theorem for formal propositional logic with respect to the variety of L?b algebras. We show that the variety of L?b algebras has the weak amalgamation property. Some interesting subclasses of the variety of L?b algebras, e.g. linear, faithful and strongly linear L?b algebras are introduced.