Dialectica Logical Principles

Gödel’ s Dialectica interpretation was designed to obtain a relative consistency proof for Heyting arithmetic, be used in conjunction with the double negation of Peano arithmetic. In recent years, theoretic transformations (so-called interpretations) that are based on Gödel’s have been systematically extract new content from proofs and so has found relevant applications several areas mathematics computer science. Following our previous work ‘Gödel fibrations’, we present (hyper)doctrine characterisation which corresponds exactly logical description interpretation. To show derive soundness implication connective, as expounded by Spector Troelstra, categorical model. This requires extra principles, going beyond intuitionistic logic, namely Markov’s Principle (MP) Independence Premise (IP) principle, well some choice. We how these principles satisfied setting, establishing tight (internal language) correspondence between system framework. should come handy not only when discussing already known, like its use computational (some) classical theorems (proof mining), help model specific abstract machines, etc. but also devise applications.