More on SOP 1 and SOP 2

Annals of Pure and Applied Logic 155 (1):16-31 (2008)

Abstract
This paper continues the work in [S. Shelah, Towards classifying unstable theories, Annals of Pure and Applied Logic 80 229–255] and [M. Džamonja, S. Shelah, On left triangle, open*-maximality, Annals of Pure and Applied Logic 125 119–158]. We present a rank function for NSOP1 theories and give an example of a theory which is NSOP1 but not simple. We also investigate the connection between maximality in the ordering left triangle, open* among complete first order theories and the SOP2 property. We prove that left triangle, open*-maximality implies SOP2 and obtain certain 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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DOI 10.1016/j.apal.2008.02.003
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References found in this work BETA

Toward Classifying Unstable Theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.
On ◁∗-Maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.

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