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

TL;DR

This paper extends the Generic Model Theorem to equivariant presheaves, introduces new generic cohomologies, and demonstrates their simplification to non-standard cohomologies in certain cases, advancing the understanding of equivariant sheaf cohomology.

Contribution

It generalizes the Generic Model Theorem for equivariant structures and introduces a new class of generic cohomologies, connecting them to non-standard cohomologies.

Findings

Extended the Generic Model Theorem to equivariant presheaves

Introduced a new class of generic cohomologies

Showed simplification to non-standard cohomologies in examples

Abstract

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.