We show that the ℵ0-categorical structures produced by Hrushovski's predimension construction with a control function fit neatly into Shelah's SOPn hierarchy: if they are not simple, then they have SOP3 and NSOP4. We also show that structures produced without using a control function can be undecidable and have SOP.
"Some remarks on generic structures." J. Symbolic Logic 74 (4) 1143 - 1154, December 2009. https://doi.org/10.2178/jsl/1254748684