Characterization of discriminator varieties
نویسندگان
چکیده
منابع مشابه
Decidable Discriminator Varieties from Unary Varieties
We determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.
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Let /C be a class of (universal) algebras of fixed type. /C* denotes the class obtained by augmenting each member of K, by the ternary discriminator function (/(x,y, z) = x if x / ?/, ^(x,x,z) = 2:), while V(/C*) is the closure of /C* under the formation of subalgebras, homomorphic images, and arbitrary Cartesian products. For example, the class of Boolean algebras is definitionally equivalent ...
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We determine those universal classes of lattices which generate a decidable discriminator variety when augmented by a ternary discriminator term. They are the locally finite universal classes whose finite members are almost homogeneous.
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The theory of discriminator algebras and varieties has been investigated extensively, and provides us with a wealth of information and techniques applicable to specific examples of such algebras and varieties. Here we give several such examples for Boolean algebras with a residuated binary operator, abbreviated as r-algebras. More specifically, we show that all finite r-algebras, all integral r...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05627-6