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 …

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 …

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 …

This thesis is about fields with operators, through the point of view of algebra and model
theory. The two prototypical examples of fields with operators are differential fields (ie fields …