M. Aschenbrenner

Publications (2)0 Total impact

• Source

  Available from: ArXiv

  Article: Vapnik-Chervonenkis density in some theories without the independence property, I

  M. Aschenbrenner, A. Dolich, D. Haskell, D. Macpherson, S. Starchenko
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  ABSTRACT: We recast the problem of calculating Vapnik-Chervonenkis (VC) density into one of counting types, and thereby calculate bounds (often optimal) on the VC density for some weakly o-minimal, weakly quasi-o-minimal, and $P$-minimal theories.
  09/2011;
• Source

  Available from: ArXiv

  Article: Vapnik-Chervonenkis density in some theories without the independence property, II

  M. Aschenbrenner, A. Dolich, D. Haskell, D. Macpherson, S. Starchenko
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  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.
  09/2011;