ТЕОРИЯ КЛАССОВ

Classes, Theory of

A logical theory. Main concepts: class, an element of class. Main propositions: an element of class (x) is a member of the class (A) (in symbols: x ∈ A); the universal class (1) complements the null (or empty) class; relations between classes are of four types: of two arbitrary classes A and B, either A is included in B (as its subclass) or vice versa, for instance A⊂B and B⊂A; or A and B coincide partially or have no common elements at all.

Theory of Classes determines the following operations involving classes: (1) intersection A∩B, i.e., the formation of a new class out of the elements common both to A and B; (2) union A∪B, i.e., the formation of a class, whose elements belong either to A or to B, or to both; (3) complementation of A, i.e., the formation of a class out of all the elements of the universal class which are not included in A.

The laws governing the relations between classes and the operations involving them are treated in the so-called calculus of classes, which is one of the interpretations (see Interpretation and Model) of algebra of logic. At the same time the calculus of classes is treated as the calculus of singular predicates, since the expression x∈A corresponds to a propositional function.

«Борьба классов»

Исторический научно-популярный ежемесячный журнал. Выходил в Москве с марта 1931 до конца 1936. Ответственный редактор М. Н. Покровский, затем Б. М. Волин. Наибольшее внимание уделял истории революционного движения в России и других странах, истории ВКП (б) и Коммунистического Интернационала, событиям Октябрьской революции и Гражданской войны, истории фабрик и заводов. Наряду со статьями публиковались исторические документы, воспоминания политических деятелей, информация о работе научных учреждений, методические и критико-библиографические материалы, иллюстрации. В 1937 переименован в «Исторический журнал».