 Among his mathematical achievements at the decade’s close is the proof of the consistency of both the Axiom of Choice and Cantor’s Continuum Hypothesis with the Zermelo-Fraenkel axioms for set theory, obtained in 1935 and 1937, respectively. Gödel also published a number of significant papers on modal and intuitionistic logic and arithmetic during this period, principal among which is his “On intuitionistic arithmetic and number theory,” (Gödel 1933e), in which he showed that classical first order arithmetic is interpretable in Heyting arithmetic by a simple translation. Other publications of the 1930s include those on the decision problem for the predicate calculus, on the length of proofs, and on differential and projective geometry.