# Axiom:Axiom of the Empty Set/Class Theory

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## 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: $A_3$