On VC-Density in VC-Minimal Theories

Notre Dame Journal of Formal Logic 63 (3):395-413 (2022)
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Abstract

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 acleq= dcleq, 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).

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10.1215/00294527-2022-0019

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Forking in VC-minimal theories.Sarah Cotter & Sergei Starchenko - 2012 - Journal of Symbolic Logic 77 (4):1257-1271.
On VC-minimal theories and variants.Vincent Guingona & Michael C. Laskowski - 2013 - Archive for Mathematical Logic 52 (7-8):743-758.
Convexly orderable groups and valued fields.Joseph Flenner & Vincent Guingona - 2014 - Journal of Symbolic Logic 79 (1):154-170.

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