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,θ\theta, on the algebra of terms,F(ω)F(\omega ), such thatF(ω)/θF(\omega )/\thetabelongs to the given class of algebras. Thus, they are direct analogs of G. Birkhoff’s proof of the completeness theorem for equational logic.
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