Peano Arithmetic may not be interpretable in the monadic theory of orders
Shmuel Lifsches, Saharon Shelah
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 show here that it is consistent that there is no interpretation even in the monadic second-order theory of all chains.
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