Completeness theorems for universal and implicational logics of algebras via congruences
Robert W. Quackenbush · Proceedings of the American Mathematical Society · 1988
In this paper, simple algebraic proofs are given for the completeness theorems for the implicational and universal logics of algebras. The proofs are obtained by examining congruences, θ \theta , on the algebra of terms, F ( ω ) F(\omega ) , such that F ( ω ) / θ F(\omega )/\theta belongs to the given class of algebras. Thus, they are direct analogs of G. Birkhoff’s proof of the completeness theorem for equational logic.