TITLE:
Second-Order Formulas in Action
AUTHORS:
Yuri Movsisyan
KEYWORDS:
Boolean Algebra, Boolean Function, Distributive Lattice, Monotone Boolean Function, De Morgan Algebra, De Morgan Function, Boole-De Morgan Algebra, Quasi-De Morgan Function, Hyperidentity, Coidentity
JOURNAL NAME:
Applied Mathematics,
Vol.15 No.9,
September
27,
2024
ABSTRACT: This survey article illustrates many important current trends and perspectives for the field and their applications, of interest to researchers in modern algebra, mathematical logic and discrete mathematics. It covers a number of directions, including completeness theorem and compactness theorem for hyperidentities; the characterizations of the Boolean algebra of n-ary Boolean functions and the bounded distributive lattice of n-ary monotone Boolean functions; the functional representations of finitely-generated free algebras of various varieties of lattices via generalized Boolean functions, etc.