Journal of Symbolic Logic 65 (3):1014-1030 (2000)

Abstract
We show that true first-order arithmetic is interpretable over the real-algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras. From this the undecidability of the structures follows. We also show that Scott's model is equivalent to true second-order arithmetic. In the appendix we argue that undecidability on the language of ordered rings follows from intuitionistically plausible properties of the real numbers.
Keywords undecidability  intuitionistic analysis  topological models  Kripke's scheme
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DOI http://projecteuclid.org/euclid.jsl/1183746167
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References found in this work BETA

Intuitionism, an Introduction.A. Heyting - 1958 - Studia Logica 7:277-278.
Mathematical Intuitionism. Introduction to Proof Theory.A. G. Dragalin & E. Mendelson - 1990 - Journal of Symbolic Logic 55 (3):1308-1309.
A Topological Model for Intuitionistic Analysis with Kripke's Scheme.M. D. Krol - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (25-30):427-436.
A New Model for Intuitionistic Analysis.Philip Scowcroft - 1990 - Annals of Pure and Applied Logic 47 (2):145-165.

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