  We discuss and prove a theorem which asserts that any n-dimensional
semi-Riemannian manifold can be locally embedded in a (n+1)-dimensional space
with a non-degenerate Ricci tensor which is equal, up to a local analytic
diffeomorphism, to the Ricci tensor of an arbitrary specified space. This may
be regarded as a further extension of the Campbell-Magaard theorem. We
highlight the significance of embedding theorems of increasing degrees of
generality in the context of higher dimensional spacetimes theories and
illustrate the new theorem by establishing the embedding of a general class of
Ricci-flat spacetimes.
