MathGloss

A field or algebra of subsets of a set XX is a pair (X,F)(X, \mathcal F) consisting of the set XX and a collection F\mathcal F of subset of XX such that

  1. F\mathcal F is closed under complementation: XFFX\setminus F \in \mathcal F for all FFF \in \mathcal F;
  2. F\mathcal F contains the empty set.
  3. F\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