Axiom:Axiom of Unions/Class Theory

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

• Equivalence of Formulations of Axiom of Unions

• Axiom:Axiom of Unions (Set Theory)

• 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]