Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-25T17:27:46.550Z Has data issue: false hasContentIssue false
  • English
  • Français

On the strength of the interpretation method

Published online by Cambridge University Press:  12 March 2014

Yuri Gurevich  and
Saharon Shelah
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
Get access Rights & Permissions [Opens in a new window]

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
Information
The Journal of Symbolic Logic , Volume 54 , Issue 2 , June 1989 , pp. 305 - 323
Copyright
Copyright © Association for Symbolic Logic 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[Ba]Baur, W., Undecidability of the theory of abelian groups with a subgroup, Proceedings of the American Mathematical Society, vol. 55 (1976), pp. 125–128.CrossRefGoogle Scholar
[Gr]Grzegorczyk, A., Undecidability of some topological theories, Fundamenta Mathematicae, vol. 38 (1951), pp. 137–152.CrossRefGoogle Scholar
[Gu1]Gurevich, Y., Modest theory of short chains. I, this Journal, vol. 44 (1979), pp. 481–490.Google Scholar
[Gu2]Gurevich, Y., Monadic second-order theories, Model-theoretical logics (Barwise, J. and Feferman, S., editors), Springer-Verlag, Berlin, 1985, pp. 479–506.Google Scholar
[GS]Gurevich, Y. and Shelah, S., The monadic theory and the “next world”, Israel Journal of Mathematics, vol. 49 (1984), pp. 55–68.CrossRefGoogle Scholar
[Ra]Ramsey, F. P., On a problem of formal logic, Proceedings of the London Mathematical Society, ser. 2, vol. 30 (1930), pp. 264–286.CrossRefGoogle Scholar
[Sh]Shelah, S., The monadic theory of order, Annals of Mathematics, ser. 2, vol. 102 (1975), pp. 379–419.CrossRefGoogle Scholar
[TMR]Tarski, A., Mostowski, A. and Robinson, R. M., Undecidable theories, North-Holland, Amsterdam, 1953.Google Scholar