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Axiomatizability of a projection of a universally axiomatizable class of algebraic systems

✍ Scribed by R. R. Shagidullin

Publisher
Springer US
Year
1988
Tongue
English
Weight
279 KB
Volume
40
Category
Article
ISSN
1573-8795

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SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let Ο‰ ≀ Ξ± < Ξ² and let K ∈ {SC, CA, QA, QEA}. We show that the class of Ξ±-dimensional neat reducts of algebras in K

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In classes of algebras such as lattices, groups, and rings, there arefinite algebras which individually generate quasivarieties which are not finitely axiomatiza.ble (see [2], [3], [8]). We show here that this kind of algebras also exist in Heyting algebras as well as in topological Boolean algebras