Triposes and Gödel's Dialectica Interpretation

Explore the semantic presentation of Gödel's Dialectica interpretation through the lens of categorical structures in this 30-minute lecture by Giuseppe Rosolini. Delve into the use of triposes, introduced by Hyland, Johnstone, and Pitts in 1980, to address the problem of semantically representing Gödel's functional interpretation. Examine the joint work of Rosolini and colleagues, including Biering, Birkedal, Butz, Hyland, van Oosten, and Streicher, on this topic. Discover how appropriate categories can be utilized to study the Dialectica interpretation and consider potential solutions to a question posed by P. Oliva. Gain insights into the intersection of category theory, logic, and mathematical foundations in this advanced talk presented as part of the Hausdorff Trimester Program on Types, Sets and Constructions at the Hausdorff Center for Mathematics.