Undecidability of the real-algebraic structure of models of intuitionistic elementary analysis

Journal of Symbolic Logic 65 (3):1014-1030 (2000)
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 03-D35   03-F55   Undecidability   Intuitionism   Heyting Algebra   True Second-Order Arithmetic
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