# Definition:Supercomplete Class

## Definition

Let $A$ denote a class.

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

 $(1)$ $:$ $A$ is transitive: $\ds \forall x: \forall y:$ $\ds \paren {x \in y \land y \in A \implies x \in A}$ $(2)$ $:$ $A$ is swelled: $\ds \forall x: \forall y:$ $\ds \paren {x \subseteq y \land y \in A \implies x \in A}$

## Also see

• Results about supercomplete classes can be found here.