Submission date: 4 March 2017

Abstract:

We investigate a theory of models equipped which an action of a fixed group G. We show that under the assumption of stability of the basic theory (and few other assumptions) the arising model companion of the theory of models equipped with an action of G is simple and eliminates quantifiers up to some existential formulas - similar to ACFA. Moreover, it codes finite sets and allows geometric elimination of imaginaries, but not always weak elimination of imaginaries. As a side product of our description we give a refreshed concept of PAC substructure and generalize definition of regular extensions from the algebra of fields. It turns out that the regular extensions in the stable context imply unique extensions of types.

Mathematics Subject Classification: 03C95, 03C50, 03C52

Keywords and phrases:

Full text arXiv 1703.01376: pdf, ps.