Definition:Class Intersection/Class of Sets

Definition
Let $\Bbb C$ be a class of sets.

The intersection of $\Bbb C$ is:
 * $\ds \bigcap \Bbb C := \set {x: \forall S \in \Bbb C: x \in S}$

That is, the class of all objects that are elements of all the elements of $\Bbb C$.

Thus:
 * $\ds \bigcap \set {S, T} := S \cap T$

Also see

 * Intersection of Class of Sets is Set