• Title/Summary/Keyword: Mostowski-Shepherdson mapping theorem

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A reconstruction of the G$\ddot{o}$del's proof of the consistency of GCH and AC with the axioms of Zermelo-Fraenkel set theory

  • Choi, Chang-Soon
    • Journal for History of Mathematics
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    • v.24 no.3
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    • pp.59-76
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    • 2011
  • Starting from a collection V as a model which satisfies the axioms of NBG, we call the elements of V as sets and the subcollections of V as classes. We reconstruct the G$\ddot{o}$del's proof of the consistency of GCH and AC with the axioms of Zermelo-Fraenkel set theory by using Mostowski-Shepherdson mapping theorem, reflection principles in Tarski-Vaught theorem and Montague-Levy theorem and the fact that NBG is a conservative extension of ZF.