On Löb algebras

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 Lob algebras. We show that the variety of Lob algebras has the weak amalgamation property. Some interesting subclasses of the variety of Lob algebras, e.g. linear, faithful and strongly linear Lob algebras are introduced. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)