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 prove some results about the model theory of fields with a derivation of the Frobenius
map, especially that the model companion of this theory is axiomatizable by axioms used by …

This thesis is primarily concerned with D-fields. These structures were introduced by Rahim
Moosa and Thomas Scanlon in their trilogy [51, 52, 53] in order to provide a common …

We prove that there exists a version of Weil descent, or Weil restriction, in the category of D-
algebras. The objects of this category are k-algebras R equipped with a homomorphism e …

Generalising the uniform companion for large fields with a single derivation, we construct a
theory $\text {UC} _ {\mathcal {D}} $ of fields of characteristic $0 $ with free operators …

Motivated by structural properties of differential field extensions, we introduce the notion of a
theory $ T $ being derivation-like with respect to another model-complete theory $ T_0 $. We …

We introduce the notion of a coordinate k \bfk‐algebra scheme and the corresponding
notion of a BB‐operator. This class of operators includes endomorphisms and derivations of …

We study model theory of fields with actions of a fixed finite group scheme. We prove the
existence and simplicity of a model companion of the theory of such actions, which …

The class of linearly ordered sets with one order preserving unary operation has the Strong
Amalgamation Property (SAP). The class of linearly ordered sets with one strict order …