Provably recursive functions of constructive and relatively constructive theories

Archive for Mathematical Logic 49 (3):291-300 (2010)
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Abstract

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 variant of Friedman’s translation. For the second group, we use Avigad’s forcing method

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References found in this work

Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
Constructivism in Mathematics: An Introduction.A. S. Troelstra & Dirk Van Dalen - 1988 - Amsterdam: North Holland. Edited by D. van Dalen.
Existence and feasibility in arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.
Interpreting classical theories in constructive ones.Jeremy Avigad - 2000 - Journal of Symbolic Logic 65 (4):1785-1812.

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