Non-standard cohomology for equivariant sheaves: The role of generic models

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.