  The constructible universe is the class  \(L = \bigcup_{\alpha\in \Ord} L_{\alpha}\); the members of \(L\) are the constructible sets. Gödel showed that (assuming the axioms of Zermelo-Fraenkel set theory ZF) the structure \((L, \in)\) is a model of ZF and also of AC as well as the Generalized Continuum Hypothesis). The relative consistency of AC with ZF follows.  