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VAPNIK-CHERVONENKIS DENSITY IN SOME THEORIES WITHOUT THE INDEPENDENCE PROPERTY, II
 

Summary: VAPNIK-CHERVONENKIS DENSITY IN SOME THEORIES
WITHOUT THE INDEPENDENCE PROPERTY, II
MATTHIAS ASCHENBRENNER, ALF DOLICH, DEIRDRE HASKELL,
DUGALD MACPHERSON, AND SERGEI STARCHENKO
For Anand Pillay, on his 60th birthday.
Abstract. We study the Vapnik-Chervonenkis (VC) density of definable families
in certain stable first-order theories. In particular we obtain uniform bounds on
VC density of definable families in finite 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.
Contents
1. Introduction 1
2. Preliminaries 5
3. Linear VC Density for Finite Rank Theories 9
4. Modules of Finite Breadth 15
5. Abelian Groups with Uniformly Bounded VC Density 28
References 47
1. Introduction
The Vapnik-Chervonenkis (VC) density and its closely related cousin, the VC dimen-
sion, are numerical parameters associated to any set system (i.e., a family of subsets of

  

Source: Aschenbrenner, Matthias - Department of Mathematics, University of California at Los Angeles

 

Collections: Mathematics