Sheaves of G-structures and generic G-models

TL;DR

This paper develops an equivariant approach to constructing generic models for presheaves of G-structures, extending model theory to structures with group actions and establishing the existence of generic G-models.

Contribution

It introduces an equivariant framework for generic models in presheaves of G-structures, a novel extension of classical model-theoretic constructions.

Findings

Every exact presheaf of G-structures has a generic G-model.

The construction preserves equivariance under the group action.

Provides a foundation for further study of G-structures in model theory.

Abstract

In this article we give an equivariant version for the construction of generic models on presheaves of structures. We deal with first order structures endowed with a suitable action of some fixed group, say $G$; we call them $G$-structures. We show that every exact presheaf of $G$-structures $\mathcal{M}$ has a generic (equivariant) $G$-model $\mathcal{M}^{^{gen}}$.