Second-Order Formulas in Action  

作　　者：Yuri Movsisyan Yuri Movsisyan(Department of Mathematics and Mechanics, Yerevan State University, Yerevan, Armenia)

机构地区：[1]Department of Mathematics and Mechanics, Yerevan State University, Yerevan, Armenia

出　　处：《Applied Mathematics》2024年第9期651-685,共35页应用数学（英文）

摘　　要：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.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.

关 键 词：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 

分 类 号：O15[理学—数学]