Axiom:Axiom of the Empty Set/Class Theory

Axiom

Let $V$ be a basic universe.

The empty class $\O$ is a set, that is:

$\O \in V$

Also known as

In the specific context of set theory, the Axiom of the Empty Set is also known as the axiom of existence, but there exists another axiom with such a name, used in a different context.

Hence it is preferable not to use that name.

Some sources refer to this as the axiom of the null set.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 3$ Axiom of the empty set: $A_3$