Boolean Constructions in Universal Algebras

ISBN-13: 9780792321170 / Angielski / Twarda / 1993 / 352 str.

A. G. Pinus

Opis

During the last few decades the ideas, methods, and results of the theory of Boolean algebras have played an increasing role in various branches of mathematics and cybernetics.
This monograph is devoted to the fundamentals of the theory of Boolean constructions in universal algebra. Also considered are the problems of presenting different varieties of universal algebra with these constructions, and applications for investigating the spectra and skeletons of varieties of universal algebras.
For researchers whose work involves universal algebra and logic.

Spis treści

Introduction. 1. Introduction. 1. Basic Notions of the Theory of Boolean Algebras. A. General Notions on Ordered Sets and Boolean Algebras. B. Interval and Superatomic Boolean Algebras. C. Rigid Boolean Algebras. D. Invariants of Countable Boolean Algebras and their Monoid. E. Mad-families and Boolean Algebras. 2. Basic Notions of Universal Algebra. 2: Boolean Constructions in Universal Algebras. 3. Boolean Powers. 4. Other Boolean Constructions. 5. Discriminator Varieties and their Specific Algebras. 6. Direct Presentation of a Variety and Algebras with a Minimal Spectrum. 7. Representation of Varieties with Boolean Constructions. 3: Varieties: Spectra, Skeletons, Categories. 8. Spectra and Categories. 9. Epimorphism Skeletons, Minimal Elements, the Problem of Cover, Universality. 10. Countable Epimorphism Skeletons of Discriminator Varieties. 11. Embedding and Double Skeletons. 12. Cartesian Skeletons of Congruence-Distributive Varieties. Appendix: 13. Elementary Theories of Congruence-Distributive Varieties Skeletons. 14. Some Theorems on Boolean Algebras. 15. On Better Quasi-Orders. References.