Set theory is the mathematical theory of sets and is associated with logic; it is also considered the study of sets (collections of objects or entities that can be real or concepts) and their properties. (For more about sets, see below.) Under formal set theory, three primitives (undefined terms) are used: S (the set), I (the identity), and E (the element). Thus, the formulas Sx, Ixy, Exy mean “x is a set,” “x is identical to y,” and “x is an element of y,” respectively.

Overall, set theory fits in with the aims of logic research: to find a single formula theory that will unify and become the basis for all of mathematics. And as it turns out, sets lead directly to a vast amount of data encompassing all of modern mathematics. There are also a number of different set theories, each having its own rules and axioms. No matter what version, set theory is not only important to mathematics and logic, but to other fields as well, such as computer technology, and atomic and nuclear physics.