About: Collapsing algebra

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

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.

Property Value
dbo:abstract
  • 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)
dbo:wikiPageExternalLink
dbo:wikiPageID
  • 43222035 (xsd:integer)
dbo:wikiPageLength
  • 2138 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1016913726 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
gold:hypernym
rdfs:comment
  • 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)
rdfs:label
  • Collapsing algebra (en)
  • 레비 붕괴 (ko)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageRedirects of
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License