Completeness Theorems for Universal and Implicational Logics of Algebras Via Congruences

Robert W. Quackenbush
1988 Proceedings of the American Mathematical Society  
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, 9, on the algebra of terms, F(oj), such that F(oj)/0 belongs to the given class of algebras. Thus, they are direct analogs of G. Birkhoff's proof of the completeness theorem for equational logic.
doi:10.2307/2047077 fatcat:k7mmg7auzvfpjknm3xmehprcdy