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Peano arithmetic may not be interpretable in the monadic theory of linear orders

Published online by Cambridge University Press:  12 March 2014

Shmuel Lifsches  and
Saharon Shelah
Shmuel Lifsches
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail: sam@math.huji.ac.il
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail: shelah@math.huji.ac.il
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Abstract

Gurevich and Shelah have shown that Peano Arithmetic cannot be interpreted in the monadic second-order theory of short chains (hence, in the monadic second-order theory of the real line). We will show here that it is consistent that the monadic second-order theory of no chain interprets Peano Arithmetic.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 3 , September 1997 , pp. 848 - 872
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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