A field or algebra of subsets of a set $X$ is a pair $(X, \mathcal F)$ consisting of the set $X$ and a collection $\mathcal F$ of subset of $X$ such that
- $\mathcal F$ is closed under complementation: $X\setminus F \in \mathcal F$ for all $F \in \mathcal F$;
- $\mathcal F$ contains the empty set.
- $\mathcal F$ is closed under binary union (with induction and De Morgan’s laws, this is euqivalent to being closed under binary intersection, finite union, and finite intersection.)
Wikidata ID: Q246506