 Gödel’s is a relative consistency proof, obtained by constructing a so-called “inner model” for ZF together with the CH. An inner model is a subcollection M of the collection V of all sets (see below) which satisfies the axioms of ZF when only sets in M are considered. Gödel’s inner model is called the inner model of constructible sets (see below) and is denoted by L. Whatever is true in an inner model is consistent with ZF for the same reason that any theory with a model is consistent. An artifact of the construction is that the Axiom of Choice (henceforth AC) is satisfied in Gödel’s inner model and hence the consistency of the AC with ZF was established by Gödel. Later on it was shown by Sierpinski that the AC is actually a consequence of the Generalized Continuum Hypothesis or the GCH, which states that for each κ, 2κ = κ+ (see Sierpinski 1947).