Gödel’s Dialectica Interpretation and Its Two-way Stretch

Abstract

Abstract In 1958, Godel published in the journal Dialectica an interpretation of intuitionistic number theory in a quantifier-free theory of functionals of finite type; this subsequently came to be known as Godel’s functional or Dialectica interpretation. The article itself was written in German for an issue of that journal in honor of Paul Bernays’ seventieth birthday. In 1965, Bernays told Godel of a plan to publish an English translation by Leo F. Boron of his 1958 paper, again in Dialectica. However, Godel was dissatisfied with certain aspects of the original, and set out to revise the translation. A year after doing so to his apparent satisfaction, Godel changed his mind and decided instead to add a new series of extensive footnotes by way of improvement and amplification. The result was sent to the printer in 1970 after much help and encouragement by Bernays and Dana Scott, but when the proof sheets were returned, Godel was again dissatisfied, especially with two of the added notes. Though he apparently worked on rewriting these until 1972, the paper was never returned in final form for publication. The corrected proof sheets found in his Nachlass were reproduced for the first time in volume 2 of Godel’s Collected Works (1990), where they appear as (1972). The full story of the vicissitudes of this paper is told by A. S. Troelstra in his introductory note to (1958) and (1972) in that volume.