Page "Complete Boolean algebra" Paragraph 0

In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum ( least upper bound ).

Complete Boolean algebras are used to construct Boolean-valued models of set theory in the theory of forcing.

Every Boolean algebra A has an essentially unique completion, which is a complete Boolean algebra containing A such that every element is the supremum of some subset of A.

As a partially ordered set, this completion of A is the Dedekind-MacNeille completion.