The study of NIP theories has received much attention from model theorists in the last
decade, fuelled by applications to o-minimal structures and valued fields. This book, the first …

We study the algebraic implications of the non-independence property and variants thereof
(dp-minimality) on infinite fields, motivated by the conjecture that all such fields which are …

We shall define a general notion of dimension, and study groups and rings whose
interpretable sets carry such a dimension. In particular, we deduce chain conditions for …

We prove that every non-trivial valuation on an infinite superrosy field of positive
characteristic has divisible value group and algebraically closed residue field. In fact, we …

We introduce a notion of Polish structure and, in doing so, provide a setting which allows the
application of ideas and techniques from model theory, descriptive set theory, topology and …

We prove that $\omega $-categorical rings with NIP are nilpotent-by-finite and that $\omega
$-categorical groups with NIP and fsg are nilpotent-by-finite, too. We give an easy proof that …

Regular groups and fields are common generalizations of minimal and quasi-minimal
groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically …

We study relationships between certain algebraic properties of groups and rings definable in
a first order structure or*-closed in a compact G-space. As a consequence, we obtain a few …

Let G be a group definable in a monster model of a rosy theory satisfying NIP. Assume that G
has hereditarily finitely satisfiable generics and 1< Ub (G)<∞. We prove that if G acts …

Definable Valuations on NIP Fields Page 1 Definable Valuations on NIP Fields Dissertation
submitted for the degree of Doctor of Natural Science Presented by Katharina Dupont at the …