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 …

We study model theory of actions of finite groups on substructures of a stable structure. We
give an abstract description of existentially closed actions as above in terms of invariants …

We show that if GG is a finitely generated group such that its profinite completion G ̂ G is
“far from being projective”(ie, the kernel of the universal Frattini cover of G ̂ G is not a small …

We give algebraic conditions for a finite commutative algebra $ B $ over a field of positive
characteristic, which are equivalent to the companionability of the theory of fields with “$ B …

For a group G, we define the notion of a G‐kernel and show that the properties of G‐kernels
are closely related with the existence of a model companion of the theory of Galois actions of …

We show that for an arbitrary stable theory T, a group G is profinite if and only if G occurs as
a Galois group of some Galois extension inside a monster model of T. We prove that any …

We show that the theory of Galois actions of a torsion Abelian group A is companionable if
and only if, for each prime p, the p-primary part of A is either finite or it coincides with the …

We study model-complete fields that avoid a given quasi-project variety $ V $. There is a
close connection between hyperbolicity of $ V $ and the existence of the model companion …

Let G be a finite group. We explore the model-theoretic properties of the class of differential
fields of characteristic zero in m commuting derivations equipped with a G-action by …

arXiv:2312.08988v1 [math.LO] 14 Dec 2023 Page 1 arXiv:2312.08988v1 [math.LO] 14 Dec
2023 OF MODEL COMPLETENESS AND ALGEBRAIC GROUPS DANIEL MAX HOFFMANN♣ …