About: Freiling's axiom of symmetry

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Freiling's axiom of symmetry is a set-theoretic axiom proposed by Chris Freiling. It is based on intuition of Stuart Davidsonbut the mathematics behind it goes back to Wacław Sierpiński. Let denote the set of all functions from to countable subsets of . The axiom states: For every , there exist such that and . Freiling claims that probabilistic intuition strongly supports this proposition while others disagree. There are several versions of the axiom, some of which are discussed below.

Attributes	Values
rdf:type	yago:WikicatAxiomsOfSetTheory yago:Abstraction100002137 yago:AuditoryCommunication107109019 yago:Communication100033020 yago:Maxim107152948 yago:Saying107151380 yago:Speech107109196
rdfs:label	Freiling's axiom of symmetry (en) Symmetrieaxioma van Freiling (nl)
rdfs:comment	De symmetrieaxioma van Freiling (AX) is een verzameling-theoretisch axioma dat werd voorgesteld door . Het is gebaseerd op de intuïtie van Stuart Davidson, maar de wiskunde erachter gaat terug op de Poolse wiskundige Wacław Sierpiński. Laat A de verzameling van functies zijn die getallen in het eenheidsinterval [0,1] afbeelden op de aftelbare deelverzamelingen in hetzelfde interval. Het axioma AX luidt als volgt: Voor elke f in A bestaat er een x en y zodanig dat x niet voorkomt in f(y) en y niet voorkomt in f(x). (nl) Freiling's axiom of symmetry is a set-theoretic axiom proposed by Chris Freiling. It is based on intuition of Stuart Davidsonbut the mathematics behind it goes back to Wacław Sierpiński. Let denote the set of all functions from to countable subsets of . The axiom states: For every , there exist such that and . Freiling claims that probabilistic intuition strongly supports this proposition while others disagree. There are several versions of the axiom, some of which are discussed below. (en)
dcterms:subject	Thought experiments Axioms of set theory
Wikipage page ID	162267 (xsd:integer)
Wikipage revision ID	1117353468 (xsd:integer)
Link from a Wikipage to another Wikipage	Thought experiments Hugo Steinhaus Complete graph Measure (mathematics) Continuum hypothesis Chris Freiling Tacit assumption Banach–Tarski paradox Wacław Sierpiński Lebesgue measure Journal of Philosophical Logic Journal of Symbolic Logic Probability Paul Cohen Axioms of set theory Freiling's axiom of symmetry Kurt Gödel Set theory Martin's axiom Vitali set
sameAs	Freiling's axiom of symmetry Freiling's axiom of symmetry Freiling's axiom of symmetry Freiling's axiom of symmetry Freiling's axiom of symmetry
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:NumBlk
has abstract	Freiling's axiom of symmetry is a set-theoretic axiom proposed by Chris Freiling. It is based on intuition of Stuart Davidsonbut the mathematics behind it goes back to Wacław Sierpiński. Let denote the set of all functions from to countable subsets of . The axiom states: For every , there exist such that and . A theorem of Sierpiński says that under the assumptions of ZFC set theory, is equivalent to the negation of the continuum hypothesis (CH). Sierpiński's theorem answered a question of Hugo Steinhaus and was proved long before the independence of CH had been established byKurt Gödel and Paul Cohen. Freiling claims that probabilistic intuition strongly supports this proposition while others disagree. There are several versions of the axiom, some of which are discussed below. (en) De symmetrieaxioma van Freiling (AX) is een verzameling-theoretisch axioma dat werd voorgesteld door . Het is gebaseerd op de intuïtie van Stuart Davidson, maar de wiskunde erachter gaat terug op de Poolse wiskundige Wacław Sierpiński. Laat A de verzameling van functies zijn die getallen in het eenheidsinterval [0,1] afbeelden op de aftelbare deelverzamelingen in hetzelfde interval. Het axioma AX luidt als volgt: Voor elke f in A bestaat er een x en y zodanig dat x niet voorkomt in f(y) en y niet voorkomt in f(x). (nl)
gold:hypernym	Axiom
prov:wasDerivedFrom	wikipedia-en:Freiling's_axiom_of_symmetry?oldid=1117353468&ns=0
page length (characters) of wiki page	10264 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Freiling's_axiom_of_symmetry
is Link from a Wikipage to another Wikipage of	List of axioms Hugo Steinhaus Freiling's Axiom of Symmetry Glossary of set theory Continuum hypothesis Chris Freiling Freiling's axiom of symmetry List of statements independent of ZFC Axiom of symmetry Freiling's axioms of symmetry Freiling axiom of symmetry
is Wikipage redirect of	Freiling's Axiom of Symmetry Axiom of symmetry Freiling's axioms of symmetry Freiling axiom of symmetry
is foaf:primaryTopic of	wikipedia-en:Freiling's_axiom_of_symmetry

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