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- Freilings_axiom_of_symmetry abstract "Freiling's axiom of symmetry (AX) 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 A be the set of functions mapping real numbers in the unit interval [0,1] to countable subsets of the same interval. The axiom AX states:For every f in A, there exist x and y such that x is not in f(y) and y is not in f(x).A theorem of Sierpiński says that under the assumptions of ZFC set theory,AX 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 propositionwhile others disagree. There are several versions of the axiom, some of whichare discussed below.".
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- Freilings_axiom_of_symmetry wikiPageOutDegree "17".
- Freilings_axiom_of_symmetry wikiPageRevisionID "674548116".
- Freilings_axiom_of_symmetry wikiPageWikiLink Banach–Tarski_paradox.
- Freilings_axiom_of_symmetry wikiPageWikiLink Category:Axioms_of_set_theory.
- Freilings_axiom_of_symmetry wikiPageWikiLink Chris_Freiling.
- Freilings_axiom_of_symmetry wikiPageWikiLink Complete_graph.
- Freilings_axiom_of_symmetry wikiPageWikiLink Continuum_hypothesis.
- Freilings_axiom_of_symmetry wikiPageWikiLink David_Mumford.
- Freilings_axiom_of_symmetry wikiPageWikiLink Freilings_axiom_of_symmetry.
- Freilings_axiom_of_symmetry wikiPageWikiLink Hugo_Steinhaus.
- Freilings_axiom_of_symmetry wikiPageWikiLink Kurt_Gödel.
- Freilings_axiom_of_symmetry wikiPageWikiLink Lebesgue_measure.
- Freilings_axiom_of_symmetry wikiPageWikiLink Martins_axiom.
- Freilings_axiom_of_symmetry wikiPageWikiLink Measure_(mathematics).
- Freilings_axiom_of_symmetry wikiPageWikiLink Paul_Cohen.
- Freilings_axiom_of_symmetry wikiPageWikiLink Probability.
- Freilings_axiom_of_symmetry wikiPageWikiLink Set_theory.
- Freilings_axiom_of_symmetry wikiPageWikiLink Vitali_set.
- Freilings_axiom_of_symmetry wikiPageWikiLink Wacław_Sierpiński.
- Freilings_axiom_of_symmetry wikiPageWikiLinkText "Freiling's axiom of symmetry".
- Freilings_axiom_of_symmetry wikiPageWikiLinkText "Freiling's_axiom_of_symmetry".
- Freilings_axiom_of_symmetry wikiPageWikiLinkText "above".
- Freilings_axiom_of_symmetry wikiPageUsesTemplate Template:Citation.
- Freilings_axiom_of_symmetry wikiPageUsesTemplate Template:Cite_journal.
- Freilings_axiom_of_symmetry wikiPageUsesTemplate Template:Harv.
- Freilings_axiom_of_symmetry wikiPageUsesTemplate Template:NumBlk.
- Freilings_axiom_of_symmetry subject Category:Axioms_of_set_theory.
- Freilings_axiom_of_symmetry hypernym Axiom.
- Freilings_axiom_of_symmetry type Redirect.
- Freilings_axiom_of_symmetry comment "Freiling's axiom of symmetry (AX) 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 A be the set of functions mapping real numbers in the unit interval [0,1] to countable subsets of the same interval.".
- Freilings_axiom_of_symmetry label "Freiling's axiom of symmetry".
- Freilings_axiom_of_symmetry sameAs Q2276975.
- Freilings_axiom_of_symmetry sameAs Symmetrieaxioma_van_Freiling.
- Freilings_axiom_of_symmetry sameAs m.015jz3.
- Freilings_axiom_of_symmetry sameAs Q2276975.
- Freilings_axiom_of_symmetry wasDerivedFrom Freilings_axiom_of_symmetry?oldid=674548116.
- Freilings_axiom_of_symmetry isPrimaryTopicOf Freilings_axiom_of_symmetry.