Peano Arithmetic may not be interpretable in the monadic theory of orders
Shmuel Lifsches, Saharon Shelah · arXiv (Cornell University) · 1993
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.