Model theory, a major branch of mathematical logic, plays a key role connecting logic and
other areas of mathematics such as algebra, geometry, analysis, and combinatorics …

ONE-DIMENSIONAL ASYMPTOTIC CLASSES OF FINITE STRUCTURES 1. Introduction
Dimension theory, so-called, has become a pervasive them Page 1 TRANSACTIONS OF THE …

arXiv:1009.5421v1 [math.LO] 28 Sep 2010 Page 1 arXiv:1009.5421v1 [math.LO] 28 Sep
2010 ARTIN-SCHREIER EXTENSIONS IN NIP AND SIMPLE FIELDS ITAY KAPLAN …

We continue the study of n-dependent groups, fields and related structures, largely
motivated by the conjecture that every n-dependent field is dependent. We provide evidence …

We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on
an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are …

Let K be a field. The étale open topology on the K-points V (K) of a K-variety V was
introduced in [23]. The étale open topology is non-discrete if and only if K is large. If K is …

In this article we survey a body of results about classes of finite first order structures in which
definable sets have a rather uniform asymptotic behaviour. Non-principal ultraproducts of …

This is a survey, intended both for group theorists and model theorists, concerning the
structure of pseudofinite groups, that is, infinite models of the first-order theory of finite …

In this paper, we shall study type-definable groups in a simple theory with respect to one or
several stable reducts. While the original motivation came from the analysis of definable …

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 …