I will review the concept of vc-dimension of a formula, and the vc-function of a first order theory. The concept of breadth on the lattice of PP-definable subgroups of a module will be defined, and the relationship between these notions will be explored. Some model theory of Modules will be used to refine certain questions from the paper of Aschenbrenner, Dolich, Haskell, Macpherson, and Starchenko. The talk will include several pictures and examples to clarify the notions involved.