We show that any formula with two free variables in a Vapnik–Chervonenkis (VC) minimal theory has VC-codensity at most 2. Modifying the argument slightly, we give a new proof of the fact that, in a VC-minimal theory where , the VC-codensity of a formula is at most the number of free variables (from the work of Aschenbrenner et al., the author, and Laskowski).
"On VC-Density in VC-Minimal Theories." Notre Dame J. Formal Logic 63 (3) 395 - 413, August 2022. https://doi.org/10.1215/00294527-2022-0019