We show that the ℵ 0 -categorical structures produced by Hrushovski's predimension construction with a control function fit neatly into Shelah's SOP n hierarchy: if they are not simple, then they have SOP 3 and NSOP 4 . We also show that structures produced without using a control function can be undecidable and have SOP .
No takes yet. Share an insight, caveat, or question.
Evans et al. (2009) studied this question.