Hyperidentities: Boolean And De Morgan Structures
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A01=Yuri Movsisyan
Abelian Algebra
Author_Yuri Movsisyan
Bi-De Morgan Function
Biautomorphism
Bigroup
Bihomomorphism
Biisomorphism
Bilattice
Binary Representation
Boole-De Morgan Algebra
Boolean Function
Boolean Sum
Burnside Variety
Category=PBF
Coidentity
Complete Theory
Completeness Theorem
Congruence
De Morgan Function
De Morgan Sum
Decidability
Distributive Bilattice
Elementary Characteristic
Elementary Equivalency
Elementary Theory
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equational Theory
Essentially Hyperidentity
Field
Free De Morgan Algebra
Free Distributive Bilattice
Free Super-Boolean Algebra
Free Super-De Morgan Algebra
Functional Equation
Group
Holomorphism
Hyperalternative Algebra
Hyperassociative Algebra
Hyperequational Theory
Hyperidentity
Hypervariety of Algebras
Interlaced Bilattice
Monotone Boolean Function
Pre-Invertible Algebra
Pre-Quasigroup
Quasi-De Morgan Function
Quasigroup
Semigroup
Super-Boolean Algebra
Super-boolean Function
Super-De Morgan Algebra
Super-De Morgan Function
Termal Hyperidentity
Variety of Algebras
Weakly Idempotent Bilattice
Weakly Idempotent Lattice
Product details
- ISBN 9789811254918
- Publication Date: 18 Nov 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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Hyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.This book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of n-ary Boolean functions and the distributive lattice of n-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.While problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.
