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

Journal of Symbolic Logic 62 (3):848-872 (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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Second-order quantifiers and the complexity of theories.J. T. Baldwin & S. Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (3):229-303.
Monadic theory of order and topology in ZFC.Yuri Gurevich & Saharon Shelah - 1982 - Annals of Mathematical Logic 23 (2-3):179-198.

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