Birkhoff Theorem for Many Sorted Algebras
نویسنده
چکیده
• for all non-empty algebras A, B over S such that A and B are isomorphic and P [A] holds P [B] • for every non-empty algebra A over S and for strict non-empty subalgebra B of A such that P [A] holds P [B] • for every non-empty algebra A over S and for every congruence R of A such that P [A] holds P [A/R] • Let I be a set and F be an algebra family of I over A . Suppose that for every set i such that i ∈ I there exists an algebra A over A such that A = F(i) and P [A]. ThenP [∏F ].
منابع مشابه
On the Completeness Theorem of Many-sorted Equational Logic and the Equivalence between Hall Algebras and Bénabou Theories
The completeness theorem of equational logic of Birkhoff 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 many-sorted deduction, founded ultimately on the congruences on Hall algebras, generalized the completeness theorem of Birkhoff to the completeness theorem of many-sorted ...
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تاریخ انتشار 2004