π-system

Noun

 * 1)  A non-empty collection of subsets of a given set Ώ that is closed under non-empty finite intersections.

Usage notes

 * By convention, the empty intersection (aka nullary intersection: the "intersection of no sets") is taken to be Ώ itself: its explicit exclusion means that Ώ need not be a member of any arbitrary π-system (i.e., of every π-system).
 * The system is said to be a π-system on Ώ.
 * For any family Σ of subsets of Ώ, there exists a unique smallest π-system that contains every element of Σ: it is called the π-system generated by Σ.

Translations

 * French: π-système, pi-système
 * German: π-System
 * Italian: π-sistema, sistema pi