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On the strength of the interpretation method

Published online by Cambridge University Press:  12 March 2014

Yuri Gurevich
Affiliation:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel

Abstract

In spite of the fact that true arithmetic reduces to the monadic second-order theory of the real line, Peano arithmetic cannot be interpreted in the monadic second-order theory of the real line.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1989

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References

[Ba]Baur, W., Undecidability of the theory of abelian groups with a subgroup, Proceedings of the American Mathematical Society, vol. 55 (1976), pp. 125128.CrossRefGoogle Scholar
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[Gu2]Gurevich, Y., Monadic second-order theories, Model-theoretical logics (Barwise, J. and Feferman, S., editors), Springer-Verlag, Berlin, 1985, pp. 479506.Google Scholar
[GS]Gurevich, Y. and Shelah, S., The monadic theory and the “next world”, Israel Journal of Mathematics, vol. 49 (1984), pp. 5568.CrossRefGoogle Scholar
[Ra]Ramsey, F. P., On a problem of formal logic, Proceedings of the London Mathematical Society, ser. 2, vol. 30 (1930), pp. 264286.CrossRefGoogle Scholar
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[TMR]Tarski, A., Mostowski, A. and Robinson, R. M., Undecidable theories, North-Holland, Amsterdam, 1953.Google Scholar

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