Journal of Symbolic Logic

Undecidability of the Real-Algebraic Structure of Models of Intuitionistic Elementary Analysis

Miklos Erdelyi-Szabo

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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.

Article information

Source
J. Symbolic Logic, Volume 65, Issue 3 (2000), 1014-1030.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746167

Mathematical Reviews number (MathSciNet)
MR1791362

Zentralblatt MATH identifier
0970.03037

JSTOR
links.jstor.org

Keywords
03-D35 03-F55 Undecidability Intuitionism Heyting Algebra True Second-Order Arithmetic

Citation

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


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