A semantic approach to conservativity

Abstract

The aim of this paper is to describe from a semantic perspective the problem of conservativity of classical first-order theories over their intuitionistic counterparts. In particular, we describe a class of formulae for which such conservativity results can be proven in case of any intuitionistic theory T which is complete with respect to a class of T-normal Kripke models. We also prove conservativity results for intuitionistic theories which are closed under the Friedman translation and complete with respect to a class of conversely well-founded Kripke models. The results can be applied to a wide class of intuitionistic theories and can be viewed as generalization of the results obtained by syntactic methods.