  We generalize the Generic Model Theorem for equivariant presheaves of
structures; extending the results of Macintyre and Caicedo. We also introduce a
new class of generic cohomologies and show how, for some examples, they
simplify to non standard cohomologies.
  Key words and phrases: Generic Model Theorem, Equivariant Structures,
Equivariant Cohomology.
  Primary fields: Model Theory. Equivariant sheaf cohomology.
