Axiom of Choice is Independent of ZF



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  • 2 Proof
  • 3 Historical Note
  • 4 Sources
  • Theorem

    The Axiom of Choice can be neither proved nor disproved from the axiomsofZermelo-Fraenkel set theory.


    Proof




    Historical Note

    Kurt Gödel showed that the Axiom of Choice is not disprovable in Zermelo-Fraenkel set theory.

    Paul Cohen showed that neither is the Axiom of Choice provable in Zermelo-Fraenkel set theory.


    Sources

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    Axiom of Choice



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