Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 65, Issue 3 (2000), 1014-1030.
Undecidability of the Real-Algebraic Structure of Models of Intuitionistic Elementary Analysis
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.
J. Symbolic Logic, Volume 65, Issue 3 (2000), 1014-1030.
First available in Project Euclid: 6 July 2007
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Erdelyi-Szabo, Miklos. Undecidability of the Real-Algebraic Structure of Models of Intuitionistic Elementary Analysis. J. Symbolic Logic 65 (2000), no. 3, 1014--1030. https://projecteuclid.org/euclid.jsl/1183746167