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  1. Some Intuitionistic Equivalents of Classical Principles for Degree 2 Formulas.Stefano Berardi - 2006 - Annals of Pure and Applied Logic 139 (1):185-200.
    We consider the restriction of classical principles like Excluded Middle, Markov’s Principle, König’s Lemma to arithmetical formulas of degree 2. For any such principle, we find simple mathematical statements which are intuitionistically equivalent to it, provided we restrict universal quantifications over maps to computable maps.
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  • Provably Recursive Functions of Constructive and Relatively Constructive Theories.Morteza Moniri - 2010 - Archive for Mathematical Logic 49 (3):291-300.
    In this paper we prove conservation theorems for theories of classical first-order arithmetic over their intuitionistic version. We also prove generalized conservation results for intuitionistic theories when certain weak forms of the principle of excluded middle are added to them. Members of two families of subsystems of Heyting arithmetic and Buss-Harnik’s theories of intuitionistic bounded arithmetic are the intuitionistic theories we consider. For the first group, we use a method described by Leivant based on the negative translation combined with a (...)
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  • A Semantic Approach to Conservativity.Tomasz Połacik - 2016 - Studia Logica 104 (2):235-248.
    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 (...)
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