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On the strength of the interpretation method

  • Yuri Gurevich (a1) and Saharon Shelah (a2)

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.

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References

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[Ba]Baur, W., Undecidability of the theory of abelian groups with a subgroup, Proceedings of the American Mathematical Society, vol. 55 (1976), pp. 125128.
[Gr]Grzegorczyk, A., Undecidability of some topological theories, Fundamenta Mathematicae, vol. 38 (1951), pp. 137152.
[Gu1]Gurevich, Y., Modest theory of short chains. I, this Journal, vol. 44 (1979), pp. 481490.
[Gu2]Gurevich, Y., Monadic second-order theories, Model-theoretical logics (Barwise, J. and Feferman, S., editors), Springer-Verlag, Berlin, 1985, pp. 479506.
[GS]Gurevich, Y. and Shelah, S., The monadic theory and the “next world”, Israel Journal of Mathematics, vol. 49 (1984), pp. 5568.
[Ra]Ramsey, F. P., On a problem of formal logic, Proceedings of the London Mathematical Society, ser. 2, vol. 30 (1930), pp. 264286.
[Sh]Shelah, S., The monadic theory of order, Annals of Mathematics, ser. 2, vol. 102 (1975), pp. 379419.
[TMR]Tarski, A., Mostowski, A. and Robinson, R. M., Undecidable theories, North-Holland, Amsterdam, 1953.

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On the strength of the interpretation method

  • Yuri Gurevich (a1) and Saharon Shelah (a2)

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