A Semantic Approach to Conservativity

Studia Logica 104 (2):235-248 (2016)

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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.
Keywords Classical and intuitionistic first order theories  Conservativity  Kripke models
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DOI 10.1007/s11225-015-9639-7
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References found in this work BETA

Constructive Set Theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.
Interpreting Classical Theories in Constructive Ones.Jeremy Avigad - 2000 - Journal of Symbolic Logic 65 (4):1785-1812.
Submodels of Kripke Models.Albert Visser - 2001 - Archive for Mathematical Logic 40 (4):277-295.
Intuitionistic Validity in T-Normal Kripke Structures.Samuel R. Buss - 1993 - Annals of Pure and Applied Logic 59 (3):159-173.
Classical and Intuitionistic Models of Arithmetic.Kai F. Wehmeier - 1996 - Notre Dame Journal of Formal Logic 37 (3):452-461.

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