# Sh:471

• Lifsches, S., & Shelah, S. (1997). Peano arithmetic may not be interpretable in the monadic theory of linear orders. J. Symbolic Logic, 62(3), 848–872.
• 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.
• published version (26p)
Bib entry
@article{Sh:471,
author = {Lifsches, Shmuel and Shelah, Saharon},
title = {{Peano arithmetic may not be interpretable in the monadic theory of linear orders}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {62},
number = {3},
year = {1997},
pages = {848--872},
issn = {0022-4812},
doi = {10.2307/2275575},
mrclass = {03C85 (03E35 03F25 03F30)},
mrnumber = {1472126},
mrreviewer = {M. Yasuhara},
doi = {10.2307/2275575},
note = {\href{https://arxiv.org/abs/math/9308219}{arXiv: math/9308219}},
arxiv_number = {math/9308219}
}