In Shelah's programme of classification theory, a central rôle is played by dividing lines.  That is, the class of all theories should be divided into those having some property and those which do not and this division into these two classes should be authentic in the sense that the classes should admit various definitions of different characters.  For example, the class of stable theories may be described in many facially dissimilar ways as, for example, those theories with respect to which every type is definable, those with respect to which no formula has the order property, or those for which there is some infinite cardinal κ at least as large as that of the language for which over every model of size κ there are no more than κ many 1-types.  Many of these classification theoretic classes are defined by forbidding the existence of certain combinatorial configurations.  For example, the class of dependent or NIP (for "Not the Independence Property") theories is defined by saying that for no formula φ(x,y) is it possible to find a model M and sequences (ai)i=0∞ and (bS) where the b sequence is indexed by the subsets of the natural numbers so that φ(ai,bS) if and only if i ∈ S.  Around the same time that Shelah isolated the independence property, Vladimir Vapnik and Alexey Chervonenkis discovered the same notion in machine learning theory.  Consequences of the model theoretic analysis of NIP have since been drawn in theory of neural networks, extremal combinatorics, the theory of differential privacy, and machine learning theory more broadly. 