Journal of Symbolic Logic

Peano Arithmetic May Not be Interpretable in the Monadic Theory of Linear Orders

Shmuel Lifsches and Saharon Shelah

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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.

Article information

Source
J. Symbolic Logic, Volume 62, Issue 3 (1997), 848-872.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745300

Mathematical Reviews number (MathSciNet)
MR1472126

Zentralblatt MATH identifier
0888.03033

JSTOR
links.jstor.org

Citation

Lifsches, Shmuel; Shelah, Saharon. Peano Arithmetic May Not be Interpretable in the Monadic Theory of Linear Orders. J. Symbolic Logic 62 (1997), no. 3, 848--872. https://projecteuclid.org/euclid.jsl/1183745300


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