Definition:Greatest Set by Set Inclusion/Class Theory

Definition
Let $A$ be a class.

Then a set $M$ is the greatest element of $A$ (with respect to the subset relation) :
 * $(1): \quad M \in A$
 * $(2): \quad \forall S: \paren {S \in A \implies S \subseteq M}$

Also known as
Some sources use the term largest set or largest element. The terms are synonymous.

Also see

 * Definition:Smallest Set by Set Inclusion (Class Theory)