Functional interpretations and applications

Abstract

Functional interpretations are maps of formulas from the language of one theory into the language of another theory, in such a way that provability is preserved. These interpretations typically replace logical relations by functional relations. Functional interpretations have many uses, such as relative consistency results, conservation results, and extraction of computational content from proofs as is the case in the so-called proof mining program.

I will present several recent functional interpretations and some results that come from these interpretations. I will also give examples of application of functional interpretations, in the spirit of the proof mining program.