Axiom:Axiom of Unions

Axiom
For every set of sets, there exists a set (the sum or union set) that contains all the elements (and only those elements) that belong to at least one of the sets in the set:


 * $\forall A: \exists x: \forall y: \paren {y \in x \iff \exists z: \paren {z \in A \land y \in z} }$

Also known as
Some sources refer to this as the Axiom of the Sum Set.

Some give this a plural: Axiom of Unions.

The treatment given by in his  of $1955$ is to refer to it as the axiom of amalgamation with a view to making a greater distinction between this and his axiom of union, which is different.