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We study the variety of {\it L\"{o}b 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\"{o}b
algebras. We show that the variety of L\"{o}b algebras has the
weak amalgamation property. Some interesting subclasses of the
variety of L\"{o}b algebras, e. g. linear, faithful and strongly
linear L\"{o}b algebras are introduced.
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