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

Published online by Cambridge University Press:  12 March 2014

Miklós Erdélyi-Szabó
Miklós Erdélyi-Szabó*
Affiliation:
Mindmaker Ltd. H1121 Budapest, Konkoly Thege Mikclós Út 29–33, Hungary E-mail: mszabo@mindmaker.hu
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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

UndecidabilityIntuitionismHeyting algebraTrue second-order arithmetic
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 3 , September 2000 , pp. 1014 - 1030
Copyright
Copyright © Association for Symbolic Logic 2000

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References

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