# Axiom:Axiom of Unions/Also known as

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## Axiom of Unions: 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**.

## Sources

- 1955: John L. Kelley:
*General Topology*: Appendix: Functions: Axiom $\text{VI}$