# Definition:Swelled Class

## Definition

Let $A$ denote a class.

Then $A$ is a swelled class if and only if every subclass of every element of $A$ is also an element of $A$.

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

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

## Also see

• Results about swelled classes can be found here.