Abstract
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, $\theta$, on the algebra of terms, $F(\omega )$, such that $F(\omega )/\theta$ belongs to the given class of algebras. Thus, they are direct analogs of G. Birkhoffâs proof of the completeness theorem for equational logic.
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