n. 1. the elementary study of the properties of finite sets or classes and their relations. 2. the extension of this study to include the properties of infinite sets. 3. (Logic) a theory constructed within first-order predicate calculus that yields the mathematical theory of classes, especially one that distinguishes sets from proper classes as a means of avoiding certain paradoxes. In axiomatic set theory the consequences of various sets of axioms are studied in the abstract, while naive set theory seeks to model the intuitive properties of sets as the consequences of a set of interpreted axioms. See also Boolean algebra.