About: Tarski's theorem about choice

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

In mathematics, Tarski's theorem, proved by Alfred Tarski, states that in ZF the theorem "For every infinite set , there is a bijective map between the sets and " implies the axiom of choice. The opposite direction was already known, thus the theorem and axiom of choice are equivalent.

Property Value
dbo:abstract
  • In mathematics, Tarski's theorem, proved by Alfred Tarski, states that in ZF the theorem "For every infinite set , there is a bijective map between the sets and " implies the axiom of choice. The opposite direction was already known, thus the theorem and axiom of choice are equivalent. Tarski told Jan Mycielski that when he tried to publish the theorem in Comptes Rendus de l'Académie des Sciences Paris, Fréchet and Lebesgue refused to present it. Fréchet wrote that an implication between two well known propositions is not a new result. Lebesgue wrote that an implication between two false propositions is of no interest. (en)
dbo:wikiPageExternalLink
dbo:wikiPageID
  • 320578 (xsd:integer)
dbo:wikiPageInterLanguageLink
dbo:wikiPageLength
  • 3922 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1123353804 (xsd:integer)
dbo:wikiPageWikiLink
dbp:authorlink
  • Alfred Tarski (en)
  • Jan Mycielski (en)
dbp:first
  • Alfred (en)
  • Jan (en)
dbp:last
  • Mycielski (en)
  • Tarski (en)
dbp:wikiPageUsesTemplate
dbp:year
  • 1924 (xsd:integer)
  • 2006 (xsd:integer)
dcterms:subject
rdfs:comment
  • In mathematics, Tarski's theorem, proved by Alfred Tarski, states that in ZF the theorem "For every infinite set , there is a bijective map between the sets and " implies the axiom of choice. The opposite direction was already known, thus the theorem and axiom of choice are equivalent. (en)
rdfs:label
  • Tarski's theorem about choice (en)
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