\begin{definition}[Definition:Set Intersection/Set of Sets]
Let $\Bbb S$ be a set of sets
The '''intersection of $\Bbb S$''' is:
:$\ds \bigcap \Bbb S := \set {x: \forall S \in \Bbb S: x \in S}$
That is, the set of all objects that are elements of all the elements of $\Bbb S$.
Thus:
:$\ds \bigcap \set {S, T} := S \cap T$
\end{definition}