# Category:Axioms/Axiom of the Empty Set

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This category contains axioms related to Axiom of the Empty Set.

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.

### Set Theory

- $\exists x: \forall y: \paren {\neg \paren {y \in x} }$

### 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:

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

- $\O \in V$

where $V$ denotes the basic universe.

## Pages in category "Axioms/Axiom of the Empty Set"

The following 9 pages are in this category, out of 9 total.

### E

- Axiom:Axiom of the Empty Set
- Axiom:Axiom of the Empty Set (Class Theory)
- Axiom:Axiom of the Empty Set (Set Theory)
- Axiom:Axiom of the Empty Set/Also known as
- Axiom:Axiom of the Empty Set/Class Theory
- Axiom:Axiom of the Empty Set/Set Theory
- Axiom:Axiom of the Empty Set/Set Theory/Formulation 1
- Axiom:Axiom of the Empty Set/Set Theory/Formulation 2