# Definition:Stable under Intersection

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## Definition

Let $X$ be a set, and let $\SS \subseteq \powerset X$ be a collection of subsets of $X$.

Then $\SS$ is said to be **stable under intersection(s)**, or simply **$\cap$-stable**, if and only if:

- $\forall S, T \in \SS: S \cap T \in \SS$