# Definition:Supercomplete Class

## Definition

Let $A$ denote a class.

Then $A$ is a supercomplete class if and only if both:

$A$ is transitive

and:

$A$ is swelled.

That is, $A$ is supercomplete if and only if:

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

## Also see

• Results about supercomplete classes can be found here.