  We give an indication that gravity coupled to an infinite number of fields
might be a renormalizable theory. A toy model with an infinite number of
interacting fermions in four-dimentional space-time is analyzed. The model is
finite at any order in perturbation theory. However, perturbation theory is
valid only for external momenta smaller than $\lambda ^{-\frac{1}{2}}$ , where
$\lambda$ is the coupling constant.
