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Journal of the London Mathematical Society 1992 s2-45(2):377-384; doi:10.1112/jlms/s2-45.2.377
© 1992 by London Mathematical Society
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© Oxford University Press

Vapnik-Chervonenkis Classes of Definable Sets

Michael C. Laskowski

Mathematical Sciences Research Institute 1000 Centennial Drive Berkeley California 94720 USA

We show that a class of subsets of a structure uniformly definable by a first-order formula is a Vapnik-Chervonenkis class if and only if the formula does not have the independence property. Via this connection we obtain several new examples of Vapnik-Chervonenkis classes, including sets of positivity of finitely subanalytic functions.

Department of Mathematics University of Maryland College Park Maryland 20742 USA


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