Model theoretic dynamics in Galois fashion

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Abstract

We fix a monster model D of some stable theory and investigate substructures of D which are existentially closed within the class of substructures equipped with an action of a fixed group G. We describe them as PAC substructures of D and obtain results related to Galois theory.

Assuming that the class of these existentially closed substructures is elementary, we show that, under the assumption of having bounded models, its theory is simple and eliminates quantifiers up to some existential formulas. Moreover, this theory codes finite sets and allows a geometric elimination of imaginaries, but not always a weak elimination of imaginaries.

MSC

primary
03C95
secondary
03C45
03C50
03C52

Keywords

Model companions
Automorphisms group
Group actions

Cited by (0)

1

SDG. Part of the work on this paper was conducted during the author's internship at the Warsaw Center of Mathematics and Computer Science. Supported by NCN grants 2016/20/T/ST1/00482 and 2016/21/N/ST1/01465, and partially supported by NCN grant 2015/19/B/ST1/01150.