More on SOP1 and SOP2
Abstract
This paper continues math.LO/0009087. 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 complete the proof started in math.LO/0009087 of the fact that <*-maximality implies SOP2 and get weaker results in the other direction. The paper provides a step toward the classification of unstable theories without the strict order property.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.