zbMATH — the first resource for mathematics

Boolean constructions in universal algebra. (English. Russian original) Zbl 0792.08002
Russ. Math. Surv. 47, No. 4, 157-198 (1992); translation from Usp. Mat. Nauk 47, No. 4(286), 145-180 (1992).
Starting with the observation of the continuously growing role played by the ideas, methods, and results of the theory of Boolean algebras in various domains of mathematics and cybernetics, the aims of this survey are to introduce the definitions of Boolean constructions, to describe their basic properties, and to demonstrate their application in the study of the structure of varieties of universal algebra. So, the author gives a survey of results relative to Boolean power, other Boolean constructions, discriminator varieties, the representation of varieties by Boolean constructions, skeletons of congruence-distributive varieties and decidability problems for varieties (the problems posed in this survey and arising directly from the context do not pretend to form a complete picture of the whole range of problems related to Boolean constructions).

08-02 Research exposition (monographs, survey articles) pertaining to general algebraic systems
06E99 Boolean algebras (Boolean rings)
08B10 Congruence modularity, congruence distributivity
03C90 Nonclassical models (Boolean-valued, sheaf, etc.)
Full Text: DOI