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  1. Undecidability of the Real-Algebraic Structure of Models of Intuitionistic Elementary Analysis.Miklós Erdélyi-Szabó - 2000 - Journal of Symbolic Logic 65 (3):1014-1030.
    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.
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