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 …

Introduction to theories without the independence property Page 1 Introduction to theories
without the independence property Hans Adler∗ 4th June 2008 Abstract We present an updated …

We study definable sets, groups, and fields in the theory $ T_\infty $ of infinite-dimensional
vector spaces over an algebraically closed field equipped with a nondegenerate symmetric …

We give a general exposition of model theoretic connected components of groups. We show
that if a group G has NIP, then there exists the smallest invariant (over some small set) …

In this paper a systematic study of the category GTS of generalized topological spaces (in
the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some …

We show that any pseudofinite group with NIP theory and with a finite upper bound on the
length of chains of centralisers is soluble-by-finite. In particular, any NIP rosy pseudofinite …

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 consider groups G interpretable in a supersimple finite rank theory T such that Teq
eliminates∃∞. It is shown that G has a definable soluble radical. If G has rank 2, then if G is …

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 …

An $\mathfrak {M} _C $ group is a group in which all chains of centralizers have finite length.
In this article, we show that every nilpotent subgroup of an $\mathfrak {M} _C $ group is …