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- W2154462783 abstract "Let $mathcal {K}$ be a class of (universal) algebras of fixed type. ${mathcal {K}^t}$ denotes the class obtained by augmenting each member of $mathcal {K}$ by the ternary discriminator function $(t(x,y,z) = x$ if $x ne y,t(x,x,z) = z)$, while $vee ({mathcal {K}^t})$ is the closure of ${mathcal {K}^t}$ under the formation of subalgebras, homomorphic images, and arbitrary Cartesian products. For example, the class of Boolean algebras is definitionally equivalent to $vee ({mathcal {K}^t})$ where $mathcal {K}$ consists of a two-element algebra whose only operations are the two constants. Any equationally defined class (that is, variety) of algebras which is equivalent to some $vee ({mathcal {K}^t})$ is known as a discriminator variety. Building on recent work of S. Burris, R. McKenzie, and M. Valeriote, we characterize those locally finite universal classes $mathcal {K}$ of unary algebras of finite type for which the first-order theory of $vee ({mathcal {K}^t})$ is decidable." @default.
- W2154462783 created "2016-06-24" @default.
- W2154462783 creator A5078983016 @default.
- W2154462783 date "1993-01-01" @default.
- W2154462783 modified "2023-10-17" @default.
- W2154462783 title "Decidable discriminator varieties from unary classes" @default.
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- W2154462783 doi "https://doi.org/10.1090/s0002-9947-1993-1085938-8" @default.
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