Complete Boolean algebra is an extension of Boolean algebra that includes additional properties to ensure that every subset of its elements has a supremum (least upper bound) and an infimum (greatest lower bound).
Articles by others on the same topic
A Boolean algebra in which every set-indexed family has a join and a meet. Double-negation Boolean algebra is an intuitionistic example, with joins formed by regularizing unions. Completeness makes truth values for quantifiers possible in a Boolean-valued inner universe over intuitionistic set theory.