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Lattices of Boundedly Axiomatizable ∀-Subclasses of ∀-Classes of Universal Algebras

  • A. G. PinusEmail author
Article

The question about the structure of lattices of subclasses of various classes of algebras is one of the basic ones in universal algebra. The case under consideration most frequently concerns lattices of subvarieties (subquasivarieties) of varieties (quasivarieties) of universal algebras. A similar question is also meaningful for other classes of algebras, in particular, for universal (i.e., axiomatizable by ∀-formulas) classes of algebras. The union of two ∀-classes is itself a ∀-class, hence such lattices are distributive. As a rule, those lattices of subclasses are rather large and are not simply structured. In this connection, it is of interest to distinguish some sublattices of such lattices that would model certain properties of the lattices themselves. The present paper deals with a similar problem for ∀-classes and varieties of universal algebras.

Keywords

∀-class of universal algebras variety of universal algebras lattice of subclasses of class of algebras 

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References

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    A. G. Pinus, “On direct and inverse limits of retractive spectra,” Sib. Math. J., 58, No. 6, 1067-1070 (2017).MathSciNetCrossRefGoogle Scholar
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    H. Werner, Discriminator Algebras, Akademic-Verlag, Berlin (1978).zbMATHGoogle Scholar
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    A. G. Pinus, Conditional Terms and Their Applications in Algebra and Computation Theory [in Russian], NGTU, Novosibirsk (2002).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia

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