# 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)
• 최창순 (전북대학교 윤리교육과)
• Accepted : 2011.07.25
• Published : 2011.08.31

#### Abstract

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.

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