Abstract

Abstract. The purpose of this article is to present a parametrised functional interpretation. Depending on the choice of the parameter relations one obtains well-known functional interpretations, such as Gödel’s Dialectica interpretation, Diller-Nahm’s variant of the Dialectica interpretation, Kohlenbach’s monotone interpretations, Kreisel’s modified realizability and Stein’s family of functional interpretations. A functional interpretation consists of a formula translation and a proof translation. We show that all these interpretation only differ on two choices: firstly, on “how much ” of the counterexamples for A became witnesses for ¬A when defining the formula translation, and, secondly, “how much ” of the witnesses of A one is interested in when defining the proof translation.

Citations