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In mathematics, a collapsing algebra is a type of Boolean algebra sometimes used in forcing to reduce ("collapse") the size of cardinals. The posets used to generate collapsing algebras were introduced by Azriel Lévy in 1963. The collapsing algebra of λω is a complete Boolean algebra with at least λ elements but generated by a countable number of elements. As the size of countably generated complete Boolean algebras is unbounded, this shows that there is no free complete Boolean algebra on a countable number of elements.

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  • Collapsing algebra (en)
  • 레비 붕괴 (ko)
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  • In mathematics, a collapsing algebra is a type of Boolean algebra sometimes used in forcing to reduce ("collapse") the size of cardinals. The posets used to generate collapsing algebras were introduced by Azriel Lévy in 1963. The collapsing algebra of λω is a complete Boolean algebra with at least λ elements but generated by a countable number of elements. As the size of countably generated complete Boolean algebras is unbounded, this shows that there is no free complete Boolean algebra on a countable number of elements. (en)
  • 집합론에서, 레비 붕괴(לוי崩壞, 영어: Lévy collapse)는 강제법에서 특정한 두 기수 사이의 다른 기수들을 없애는 작용을 하는 부분 순서 집합이다. (ko)
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  • In mathematics, a collapsing algebra is a type of Boolean algebra sometimes used in forcing to reduce ("collapse") the size of cardinals. The posets used to generate collapsing algebras were introduced by Azriel Lévy in 1963. The collapsing algebra of λω is a complete Boolean algebra with at least λ elements but generated by a countable number of elements. As the size of countably generated complete Boolean algebras is unbounded, this shows that there is no free complete Boolean algebra on a countable number of elements. (en)
  • 집합론에서, 레비 붕괴(לוי崩壞, 영어: Lévy collapse)는 강제법에서 특정한 두 기수 사이의 다른 기수들을 없애는 작용을 하는 부분 순서 집합이다. (ko)
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