The Gödel Translation: History and New Directions

Explore the history and new directions of the Gödel translation in this seminar talk presented by Guram Bezhanishvili from New Mexico State University. Delve into the interpretation of intuitionistic propositional calculus as a fragment of modal logic, tracing its development from Gödel's original work in 1933 through McKinsey and Tarski's contributions in the 1940s. Examine the Blok-Esakia theorem and its significance in establishing an isomorphism between extensions of intuitionistic propositional calculus and Grzegorczyk's extension of S4. Investigate the complexities that arise when transitioning from propositional to predicate logics, including the breakdown of the Blok-Esakia isomorphism in one-variable fragments. Gain insights into open problems in this field and explore promising future research directions in this fascinating area of mathematical logic.