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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 (Department of Ethics Education, Chonbuk National University)
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Journal for History of Mathematics / v.24, no.3, 2011 , pp. 59-76 More about this Journal
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.
NBG; ZF; Mostowski-Shepherdson mapping theorem; reflection principles; constructibility; absoluteness; relative consistency;
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