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

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

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Citations of this work

Dp-minimal valued fields.Franziska Jahnke, Pierre Simon & Erik Walsberg - 2017 - Journal of Symbolic Logic 82 (1):151-165.
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.
On expansions of.Quentin Lambotte & Françoise Point - 2020 - Annals of Pure and Applied Logic 171 (8):102809.

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References found in this work

ℵ0-Categorical, ℵ0-stable structures.Gregory Cherlin, Leo Harrington & Alistair H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
On dp-minimal ordered structures.Pierre Simon - 2011 - Journal of Symbolic Logic 76 (2):448 - 460.
Dp-Minimality: Basic Facts and Examples.Alfred Dolich, John Goodrick & David Lippel - 2011 - Notre Dame Journal of Formal Logic 52 (3):267-288.
On dp-minimality, strong dependence and weight.Alf Onshuus & Alexander Usvyatsov - 2011 - Journal of Symbolic Logic 76 (3):737 - 758.
Quasi-o-minimal structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.

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