Definition:Swelled Class

Definition
Let $S$ denote a class.

Then $S$ is a swelled class every subclass of every element of $S$ is also an element of $S$.

That is, $S$ is swelled :


 * $\forall x: \forall y: \paren {x \subseteq y \land y \in S \implies x \in S}$

Also see

 * Definition:Transitive Class
 * Definition:Supercomplete Class