PREFACE

Summary

This book aims to be an introduction to model theory which can be used without any background in logic. We start from scratch, introducing first-order logic, structures, languages etc. but move on fairly quickly to the fundamental results in model theory and stability theory. We also decided to cover simple theories and Hrushovski constructions, which over the last decade have developed into an important subject. We try to give the necessary background in algebra, combinatorics and set theory either in the course of the text or in the corresponding section of the appendices. The exercises form an integral part of the book. Some of them are used later on, others complement the text or present aspects of the theory that we felt should not be completely ignored. For the most important exercises (and the more difficult ones) we include (hints for) solutions at the end of the book. Those exercises which will be used in the text have their solution marked with an asterisk.

The book falls into four parts. The first three chapters introduce the basics as would be contained in a course giving a general introduction to model theory. This first part ends with Chapter 4 which introduces and explores the notion of a type, the topology on the space of types and a way to make sure that a certain type will not be realized in a model to be constructed. The chapter ends with Fraïssé's amalgamation method, a simple but powerful tool for constructing models.