In mathematics, a field of sets is a mathematical structure consisting of a pair {\displaystyle } consisting of a set X {\displaystyle X} and a family F {\displaystyle {\mathcal {F}}} of subsets of X {\displaystyle X} called an algebra over X {\displaystyle X} that contains the empty set as an element, and is closed under the operations of taking complements in X, {\displaystyle X,} finite unions, and finite intersections. Wikipedia