 Gödel published two versions of these theorems, in 1939 and in 1940, entitled “Consistency Proof for the Generalized Continuum Hypothesis,” and “The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory,” respectively. Though completely definitive, the 1939 version is lacking in a great many details, most notably the arguments showing that if L is built inside L itself, the same L results; that is to say, the so-called absoluteness arguments are missing. Also missing are the details of the proofs that the ZF axioms hold in L. Unlike the case of the Second Incompleteness Theorem, however, Gödel subsequently gave a completely detailed proof of the two theorems in the 1940 monograph. (The 1940 proof differs substantially from the first version. For details about the two proofs and the difference between them the reader is referred to Solovay 1990 and Kanamori 2006.)