Definability in lattices of equational theoris
نویسندگان
چکیده
منابع مشابه
The equational definability of truth predicates
By a ‘logic’ we mean here a substitution-invariant consequence relation on formulas over an algebraic signature. Propositional logics are obvious examples, but even first order logic can be re-formulated in this way. The notion of an ‘algebraizable’ logic was made precise in the 1980s, mainly by Blok and Pigozzi, who provided intrinsic characterizations of the logics that are indeed algebraizab...
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We find several large classes of equations with the property that every automorphism of the lattice of equational theories of commutative groupoids fixes any equational theory generated by such equations, and every equational theory generated by finitely many such equations is a definable element of the lattice. We conjecture that the lattice has no non-identical automorphisms.
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We study first-order definability in the lattice L of equational theories of semigroups. A large collection of individual theories and some interesting sets of theories are definable in L . As examples, if T is either the equational theory of a finite semigroup or a finitely axiomatizable locally finite theory, then the set {T, T } is definable, where T ∂ is the dual theory obtained by invertin...
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1971
ISSN: 0003-4843
DOI: 10.1016/0003-4843(71)90007-6