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Complete Boolean algebra

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…

Products, Examples & Free κ-complete Boolean algebras

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FiniteAlgebra of subsetsRegular open setsTopological spacePoset
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Free κ-complete Boolean algebras

Axiom of ChoiceFreeCollapsing algebraForgetful functorLeft adjoint
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Properties of complete Boolean algebras

InfimumIf and only ifIsomorphicField of setsPower set
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The completion of a Boolean algebra

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Properties of complete Boolean algebras

The completion of a Boolean algebra

Free κ-complete Boolean algebras

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Complete Boolean algebra

Nodes60
Edges59
Triples59
Avg. degree1.97
Density0.033333
Components1

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Complete Boolean algebra

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related to Literature · 27
Complete Boolean algebra → Amsterdam, BF02757883, Bonnet, Boolean, Cambridge University Press, Donald, EMS Press, Encyclopedia, Handbook, ISBN, Israel Journal, Johnstone, Jonathan, Koppelberg, Mathematics, Monk, MR, North-Holland Publishing Co, Peter, Robert
related to Complete Boolean algebras · 10
Complete Boolean algebra → Baire, Boolean, Boolean-valued, Cantor, Every, Lebesgue, The, The Boolean, This, When
related to Free κ-complete Boolean algebras · 8
Complete Boolean algebra → Axiom, Boolean, Choice, Freyd's, In, More, This, Unless
related to Properties of complete Boolean algebras · 6
Complete Boolean algebra → Boolean, Every, For, Morgan's, Sikorski's, Stone
related to Non-complete Boolean algebras · 5
Complete Boolean algebra → Another, Boolean, Fin, The, The Boolean
related to The completion of a Boolean algebra · 2
Complete Boolean algebra → Boolean, The
is a · 1
Complete Boolean algebra → Boolean algebra in which every subset has a supremum

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boolean algebra complete set completion sets every subset algebras space supremum free finite regular element called forcing cardinal isbn subsets

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SubjectPredicateObjectConfidenceSrc
Complete Boolean algebrais aBoolean algebra in which every subset has a supremum0.90text
Complete Boolean algebrarelated to Complete Boolean algebrasEvery0.60section
Complete Boolean algebrarelated to Complete Boolean algebrasBoolean0.60section
Complete Boolean algebrarelated to Complete Boolean algebrasThe0.60section
Complete Boolean algebrarelated to Complete Boolean algebrasThis0.60section
Complete Boolean algebrarelated to Complete Boolean algebrasBoolean-valued0.60section
Complete Boolean algebrarelated to Complete Boolean algebrasWhen0.60section
Complete Boolean algebrarelated to Complete Boolean algebrasLebesgue0.60section
Complete Boolean algebrarelated to Complete Boolean algebrasThe Boolean0.60section
Complete Boolean algebrarelated to Complete Boolean algebrasBaire0.60section
Complete Boolean algebrarelated to Complete Boolean algebrasCantor0.60section
Complete Boolean algebrarelated to Free κ-complete Boolean algebrasUnless0.60section

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