Definition:Set/Class Theory

Definition

The following definition applies in the context of class theory, in which classes are the primitive objects.

A class $X$ is a set if and only if:

$\exists Y: X \in Y$

where $Y$ is a class.

Also defined as

In some formulations of class theory, classes and sets are considered distinct concepts.

This definition is only appropriate if sets do not already exist as a primitive notion.

Sources

• 2010: Elliott Mendelson: Introduction to Mathematical Logic (5th ed.): $4$ Axiomatic Set Theory