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.
More generally, if κ is a cardinal then a Boolean algebra is called κ-complete if every subset of cardinality less than κ has a supremum.
Read more about Complete Boolean Algebra: Examples, Properties of Complete Boolean Algebras, The Completion of A Boolean Algebra, Free κ-complete Boolean Algebras
Famous quotes containing the words complete and/or algebra:
“It is complete within seconds, that monument.
The blood runs underground yet brings forth a tower.
A multitude should gather for such an edifice.
For a miracle one stands in line and throws confetti.”
—Anne Sexton (19281974)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (18831955)