Field of sets
In mathematics, a field of sets is a mathematical structure consisting of a pair ( X , F ) {\displaystyle (X,{\mathcal {F}})} 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. Fields of sets should not be confused with fields in ring theory nor with fields in physics.