More on SOP₁ and SOP₂

This paper continues math.LO/0009087. 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 <^* among complete first order theories and the (N)SOP_2 property. We complete the proof started in math.LO/0009087 of the fact that <^*-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.