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

Shmuell Lifsches; Saharon Shelah

doi:10.2307/2275575

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

Shmuell Lifsches^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	848-872
Number of pages	25
Journal	Journal of Symbolic Logic
Volume	62
Issue number	3
DOIs	https://doi.org/10.2307/2275575
State	Published - Sep 1997

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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.",

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

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