More on SOP1 and SOP2

This paper continues [Sh500] and [DzSh692]. 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 among complete first order theories and the (N)SOP2 property. We prove that -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.

• Type: Journal
• Year: 2008
• Where: APAL
• Authors: Saharon Shelah, Alexander Usvyatsov
• Keywords: APAL 2008, Order Theories, Paper, Rank Function