Sh:979

• Shelah, S., & Simon, P. (2012). Adding linear orders. J. Symbolic Logic, 77(2), 717–725. arXiv: 1103.0206 DOI: 10.2178/jsl/1333566647 MR: 2963031
• Abstract:
  We address the following question: Can we expand an NIP theory by adding a linear order such that the expansion is still NIP? Easily, if acl(A)=A for all A, then this is true. Otherwise, we give counterexamples. More precisely, there is a totally categorical theory for which every expansion by a linear order has IP. There is also an \omega-stable NDOP theory for which every expansion by a linear order interprets bounded arithmetic.
• published version (10p)

@article{Sh:979,
 author = {Shelah, Saharon and Simon, Pierre},
 title = {{Adding linear orders}},
 journal = {J. Symbolic Logic},
 fjournal = {The Journal of Symbolic Logic},
 volume = {77},
 number = {2},
 year = {2012},
 pages = {717--725},
 issn = {0022-4812},
 mrnumber = {2963031},
 mrclass = {03C45 (06A05)},
 doi = {10.2178/jsl/1333566647},
 note = {\href{https://arxiv.org/abs/1103.0206}{arXiv: 1103.0206}},
 arxiv_number = {1103.0206}
}