Solution of the problem of set theory on the basis of algebra of predicates and predicate operations

Abstract

The mathematical tools of algebra of predicates and predicate operations to solve the problems in the set theory are applied in the article. The basic concepts of algebra of predicates and predicate operations, their types and formulas are considered. The quantifier algebra of predicate operations, which is complete and plays an important role in the description of operations on predicates, is considered. The basic identities and laws of quantifier algebra of predicate operations are considered. With the help of quantifier algebra of predicate operations describes the concept of linear logical operator and Galois mapping, which are usable with the capture of data quantifiers in an empty domain. The basic concepts of set theory are described. The proper interpretation of the language of algebra predicates and predicate operations received operations of union, intersection, complement, difference, symmetric difference and inclusion of sets. Some problems of set algebra are solved by means of sets of algebra of predicates and predicate operations. The advantages of using these tools to solve the problems of algebra of sets are marked.