Vapnik–Chervonenkis Density in Some Theories without the Independence Property, II

Notre Dame Journal of Formal Logic 54 (3-4):311-363 (2013)

Abstract
We study the Vapnik–Chervonenkis density of definable families in certain stable first-order theories. In particular, we obtain uniform bounds on the VC density of definable families in finite $\mathrm {U}$-rank theories without the finite cover property, and we characterize those abelian groups for which there exist uniform bounds on the VC density of definable families
Keywords theories without the independence property   Vapnik–Chervonenkis density   finite cover property   modules   abelian groups
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DOI 10.1215/00294527-2143862
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Dp-Minimal Valued Fields.Franziska Jahnke, Pierre Simon & Erik Walsberg - 2017 - Journal of Symbolic Logic 82 (1):151-165.
On VC-Minimal Fields and Dp-Smallness.Vincent Guingona - 2014 - Archive for Mathematical Logic 53 (5-6):503-517.
A New Dp-Minimal Expansion of the Integers.Eran Alouf & Christian D’elbée - 2019 - Journal of Symbolic Logic 84 (2):632-663.
The Dp-Rank of Abelian Groups.Yatir Halevi & Daniel Palacín - 2019 - Journal of Symbolic Logic 84 (3):957-986.

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