### More on ${\rm SOP}_1$ and ${\rm SOP}_2$

by Shelah and Usvyatsov. [ShUs:844]
Annals Pure and Applied Logic, 2008
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.

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