# Axiom:Axiom of Unions/Class Theory

< Axiom:Axiom of Unions(Redirected from Axiom:Axiom of Unions (Class Theory))

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## Axiom

Let $x$ be a set (of sets).

Then its union $\bigcup x$ is also a set.

## Also known as

The **axiom of unions** is in fact most frequently found with the name **axiom of union**.

However, in some treatments of axiomatic set theory and class theory, for example Morse-Kelley set theory this name is used to mean something different.

Hence $\mathsf{Pr} \infty \mathsf{fWiki}$ specifically uses the plural form **axiom of unions** for this, and reserves the singular form **axiom of union** for that.

Other terms that can be found to refer to the **axiom of unions**:

- the
**axiom of the sum set** - the
**axiom of amalgamation** - the
**union axiom**.

## Also see

- Results about
**the axiom of unions**can be found**here**.

## 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: $\S 5$ The union axiom: $A_5$**[Union axiom]**