Definition:Closure under Chain Unions

Definition

Let $A$ be a class.

$A$ is closed under chain unions if and only if:

for every chain $C$ of elements of $A$, $\bigcup C$ is also in $A$

where $\bigcup C$ denotes the union of $C$

Also see

• Results about closure under chain unions can be found here.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 2$ Superinduction and double superinduction