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.
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Połacik, T. A Semantic Approach to Conservativity. Stud Logica 104, 235–248 (2016). https://doi.org/10.1007/s11225-015-9639-7
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DOI: https://doi.org/10.1007/s11225-015-9639-7