\begin{definition}[Definition:Greatest Set by Set Inclusion/Class Theory]
Let $A$ be a class.
Then a set $M$ is the '''greatest element''' of $A$ (with respect to the subset relation) {{iff}}:
:$(1): \quad M \in A$
:$(2): \quad \forall S: \paren {S \in A \implies S \subseteq M}$
\end{definition}