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 algebraic and model-theoretic properties of existentially closed fields with an
action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a …

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 …

This thesis is concerned with developing a theory of model-theoretic tree properties. These
properties are combinatorial properties of a formula or family or formulas that place strong …

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 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 …

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 …

We consider cardinal invariants related to Shelah's model-theoretic tree properties and the
relations that obtain between them. From strong colorings, we construct theories T with κ cdt …

We consider global analogues of model-theoretic tree properties. The main objects of study
are the invariants related to Shelah's tree property $\kappa_ {\text {cdt}}(T) $, $\kappa_ {\text …

arXiv:1905.09741v1 [math.LO] 23 May 2019 Page 1 arXiv:1905.09741v1 [math.LO] 23 May
2019 PAC STRUCTURES IN NUTSHELL DANIEL MAX HOFFMANN† Instytut Matematyki …