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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.

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  • 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. (en)
  • 순서론에서 완비 불 대수(完備Boole代數, 영어: complete Boolean algebra)는 완비 격자인 불 대수이다. (ko)
  • 在数学中,完全布尔代数是所有子集都有上确界的布尔代数。完全布尔代数在力迫理论中有重要作用。任何布尔代数A都有一A是其子代数的最小的完全布尔代数。作为偏序集合,这种 A 的补全叫做。 (zh)
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  • 1839944 (xsd:integer)
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  • 9553 (xsd:nonNegativeInteger)
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  • D.A. (en)
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  • b/b016920 (en)
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  • Vladimirov (en)
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  • Boolean algebra (en)
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  • 순서론에서 완비 불 대수(完備Boole代數, 영어: complete Boolean algebra)는 완비 격자인 불 대수이다. (ko)
  • 在数学中,完全布尔代数是所有子集都有上确界的布尔代数。完全布尔代数在力迫理论中有重要作用。任何布尔代数A都有一A是其子代数的最小的完全布尔代数。作为偏序集合,这种 A 的补全叫做。 (zh)
  • 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. (en)
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  • Complete Boolean algebra (en)
  • 완비 불 대수 (ko)
  • 完全布尔代数 (zh)
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