  In Grauert's paper [G] it is noted that finite dimensionality of cohomology
groups sometimes implies vanishing of these cohomomogy groups. Later on Laufer
formulated a zero or infinity law for the cohomology groups of domains in Stein
manifolds. In this paper we generalize Laufer's Theorem in [L] and its version
for small domains of CR manifolds, proved in [Br], by considering Whitney
cohomology on locally closed subsets and cohomology with supports for currents.
With this approach we obtain a global result for CR manifolds generically
embedded in a Stein manifold. Namely a necessary condition for global embedding
into an open subset of a Stein manifold is that the de-bar-M-cohomology groups
must be either zero or infinite dimensional.
