Sh:844

• Shelah, S., & Usvyatsov, A. (2008). More on SOP_1 and SOP_2. Ann. Pure Appl. Logic, 155(1), 16–31. arXiv: math/0404178 DOI: 10.1016/j.apal.2008.02.003 MR: 2454629
• Abstract:
  This paper continues [DjSh692]. We present a rank function for NSOP_{1} theories and give an example of a theory which is NSOP_{1} but not simple. We also investigate the connection between maximality in the ordering \lhd^* among complete first order theories and the (N)SOP{}_2 property. We complete the proof started in [DjSh692] of the fact that \lhd^*-maximality implies SOP{}_2 and get weaker results in the other direction. The paper provides a step toward the classification of unstable theories without the strict order property.
• Version 2008-02-04_11 (39p) published version (16p)

@article{Sh:844,
 author = {Shelah, Saharon and Usvyatsov, Alexander},
 title = {{More on SOP$_1$ and SOP$_2$}},
 journal = {Ann. Pure Appl. Logic},
 fjournal = {Annals of Pure and Applied Logic},
 volume = {155},
 number = {1},
 year = {2008},
 pages = {16--31},
 issn = {0168-0072},
 mrnumber = {2454629},
 mrclass = {03C45},
 doi = {10.1016/j.apal.2008.02.003},
 note = {\href{https://arxiv.org/abs/math/0404178}{arXiv: math/0404178}},
 arxiv_number = {math/0404178}
}