A Guide to Classical and Modern Model Theory
Since its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. It is a lively and fertile research area which des
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TRENDS IN LOGIC Studia Logica Library VOLUME 19 Managing Editor Ryszard W6jcicki, Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland Editors Daniele Mundici, Department of Mathematics "Ulisse Dini", University of Florence, Italy Ewa Orlowska, National Institute of Telecommunications, Warsaw, Poland Graham Priest, Department of Philosophy, University of Queensland, Brisbane, Australia Krister Segerberg, Department of Philosophy, Uppsala University, Sweden Alasdair Urquhart, Department of Philosophy, University of Toronto, Canada Heinrich Wansing, Institute of Philosophy, Dresden University of Technology, Germany
SCOPE OF THE SERIES Trends in Logic is a bookseries covering essentially the same area as the journal Studia Logica - that is, contemporary formal logic and its applications and relations to other disciplines. These include artificial intelligence, informatics, cognitive science, philosophy of science, and the philosophy of language. However, this list is not exhaustive, moreover, the range of applications, comparisons and sources of inspiration is open and evolves over time.
Volume Editor Ryszard Wojacki
The titles published in this series are listed at the end of this volume.
A GUIDE TO CLASSICAL AND MODERN MODEL THEORY by
ANNALISA MARCJA University of Florence, Italy and
CARLO TOFFALORI University of Camerino, Italy
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
A CLP. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4020-1331-7 ISBN 978-94-007-0812-9 (eBook) DOI 10.1007/978-94-007-0812-9
Printed an acid-free paper
AII Rights Reserved © 2003 Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 2003 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilm ing, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
Preface This book deals with Model Theory. So the first question that a possible, recalcitrant reader might ask is just: What is Model Theory? Which are its intents and applications? Why should one try to learn it? Another, more particular question might be the following one. Let us assume, if you like, that Model Theory deserves some attention. Why should one use this book as a guide to it? The answer to the former question may sound problematic, but it is quite simple, at least in our opinion. For, Model Theory has been developing, since its birth, a number of methods and concepts that do have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. We could mention here its role in Algebra and Algebraic Geometry, for instance the analysis of differentially closed fields (and the results on the differential closure of a differential field
