turkmath.org

I will present results from my joint project with Piotr Kowalski. It is about a model-theoretic description of actions of a fixed finite group on quite arbitrary structures. More precisely, take a big model M of some stable theory and a group G. Consider the family of all substructures of M equipped with a group action (by automorphisms) of G. The question is whether the sub-family of existentially closed (i.e. rich in "solutions of equations") substructures with a group action of G can be axiomatized, so whether we can first order statements which correspond to being rich in solutions. We will analyze the situation for finite G and express the problem in terms involving only the invariants of the group action.