Notes on the Generalized Continuum Hypothesis(GCH) and ZFC system

Yufan Qian

December 28, 2017

Abstract: In this paper, starting from K.Godel[1], we prove that the generalized continuum hypothesis holds if there is no contradiction in the ZFC system. Furthermore, we combine the above conclusion with the results in P.J. Cohen[2] and then come to the conclusion that the ZFC is a system of contradiction.

Key Words: the ZFC system, ordinals, cardinals, the generalized continuum hypothesis

Notes on the Generalized Continuum Hypothesis(GCH) and ZFC system.pdf