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  • Print publication year: 1997
  • Online publication date: May 2010

Introduction

Summary

The articles in this volume demonstrate the wide variety of interactions between algebra (particularly group theory) and current research in model theory. On the one hand, the analysis of direct questions about the first-order theories of classes of algebraic structures requires an interplay between model-theoretic and algebraic methods, and often such questions also evolve into ones which are interesting from a purely algebraic viewpoint. More indirectly, the model-theoretic analysis of classes of structures using some of the latest developments of model theory (particularly stability theory) has recently resulted in a wave of new applications of model theory to other parts of mathematics.

Alongside these developments there has been considerable interaction between model theory and the study of infinite permutation groups. Automorphism groups of model-theoretically interesting structures have provided a rich supply of examples and problems for the permutation group theorists, and the study of automorphism groups has been a crucial tool in certain model-theoretic questions.

Readers can judge for themselves the extent to which the articles in this volume fit into this pattern, but I shall give a brief sketch of them, emphasising the interactions between model theory and other parts of mathematics.

The article by Evans, Ivanov and Macpherson is a survey largely concerned with a question that originated in studying the fine detail of totally categorical structures, but which is now seen (and studied) as a problem about infinite permutation groups.