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.
  • 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是重要的。对于所有布尔代数 A 都有 A 是其子代数的一个最小的完全布尔代数。作为偏序集合，这种 A 的补全叫做戴德金补全。
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  • D.A.
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  • b/b016920
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  • Vladimirov
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  • Functional completeness
  • a type of mathematical structure
  • complete sets of Boolean operators
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  • Boolean algebra
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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.
  • 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是重要的。对于所有布尔代数 A 都有 A 是其子代数的一个最小的完全布尔代数。作为偏序集合，这种 A 的补全叫做戴德金补全。
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  • Complete Boolean algebra
  • 完全布尔代数
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