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Birkhoff's completeness theorem of equational logic asserts the coincidence of the model-theoretic and proof-theoretic consequence relations. Goguen and Meseguer, giving a sound and adequate system of inference rules for finitary many-sorted equational deduction, generalized the completeness theorem of Birkhoff to the completeness of finitary many-sorted(More)
A b s t r a c t. For, not necessarily similar, single-sorted algebras Fujiwara defined, through the concept of family of basic mapping-formulas between single-sorted signatures, a notion of morphism which generalizes the ordinary notion of homomorphism between algebras. Subsequently he also defined an equivalence relation, the relation of conjugation, on(More)
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