Axiom:Axiom of the Empty Set

Axiom
The axiom of the empty set posits the existence of a set which has no elements.

Depending on whether this axiom is declared in the context of set theory or class theory, it exists in different forms.

Class Theory
In class theory, the existence of the empty class is not axiomatic, as it has been derived from previous axioms.

Hence the axiom of the empty set takes this form:

where $V$ denotes the basic universe.

Also see

 * Definition:Zermelo-Fraenkel Axioms
 * Definition:Empty Set
 * Empty Set is Unique
 * If Set Exists then Empty Set Exists