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More on SOP_1 and SOP_2

Saharon Shelah·Alex Usvyatsov
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Abstract

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.

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Saharon Shelah, Alex Usvyatsov. 2004-04-08. More on SOP_1 and SOP_2. https://arxiv.org/abs/math/0404178

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