# 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)

Bib entry

@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} }