Sh:527

• Lifsches, S., & Shelah, S. (1999). Random graphs in the monadic theory of order. Arch. Math. Logic, 38(4-5), 273–312. arXiv: math/9701219 DOI: 10.1007/s001530050129 MR: 1697962
• Abstract:
  We continue the works of Gurevich-Shelah and Lifsches-Shelah by showing that it is consistent with ZFC that the first-order theory of random graphs is not interpretable in the monadic theory of all chains. It is provable from ZFC that the theory of random graphs is not interpretable in the monadic second order theory of short chains (hence, in the monadic theory of the real line).
• published version (40p)

@article{Sh:527,
 author = {Lifsches, Shmuel and Shelah, Saharon},
 title = {{Random graphs in the monadic theory of order}},
 journal = {Arch. Math. Logic},
 fjournal = {Archive for Mathematical Logic},
 volume = {38},
 number = {4-5},
 year = {1999},
 pages = {273--312},
 issn = {0933-5846},
 doi = {10.1007/s001530050129},
 mrclass = {03C15 (03C64 03C65 03E35 05C80)},
 mrnumber = {1697962},
 mrreviewer = {John T. Baldwin},
 doi = {10.1007/s001530050129},
 note = {\href{https://arxiv.org/abs/math/9701219}{arXiv: math/9701219}},
 arxiv_number = {math/9701219},
 conference = {Logic Colloquium '95 (Haifa)}
}