Definition:Supercomplete Class

Definition
Let $S$ denote a class.

Then $S$ is a supercomplete class both:


 * $A$ is transitive

and:
 * $A$ is swelled

That is, $S$ is supercomplete :


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

Also see

 * Definition:Transitive Class
 * Definition:Swelled Class