  It is shown how tools from the area of Model Theory, specifically from the
Theory of o-minimality, can be used to prove that a class of functions is
VC-subgraph (in the sense of Dudley, 1987), and therefore satisfies a uniform
polynomial metric entropy bound. We give examples where the use of these
methods significantly improves the existing metric entropy bounds. The methods
proposed here can be applied to finite dimensional parametric families of
functions without the need for the parameters to live in a compact set, as is
sometimes required in theorems that produce similar entropy bounds (for
instance Theorem 19.7 of van der Vaart, 1998).
