Constructible Sets in Real Geometry
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A Series of Modern Surveys in Mathematics
Editorial Board
E. Bombieri, Princeton S. Feferman, Stanford M. Gromov, Bures-sur-Yvette J. Jost, Bochum H.W. Lenstra, Jr., Berkeley P.-L. Lions, Paris R. Remmert (Managing Editor), MUnster W. Schmid, Cambridge, Mass. J-P. Serre, Paris J.Tits, Paris
Volume 33
Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo
Carlos Andradas Ludwig Brocker Jesus M. Ruiz
Constructible Sets in Real Geometry
,
Springer
Carlos Andradas Departamento de Algebra Universidad Complutense de Madrid E-28040 Madrid Spain e-mail: [email protected] Ludwig Brocker Mathematisches Institut Universitat MUnster EinsteinstraBe 62 D-48149 MUnster Germany e-mail: [email protected] Jesus M. Ruiz Departamento de Geometria y Topolog'la Universidad Complutense de Madrid E-28040 Madrid Spain e-mail: [email protected] Library of Congress Cataloging-in-Publication Data Ardradas. Car 1as.
Constructible sets in real geometry! Carlos Andradas, Ludwig Br6cker, Jes~s M. quiz. p. em. -- (Ergebnisse der MathematIk und ihrer Grenzgebiete 3. Feige, Bd. 33) Includes bibl iographical rE!fere:1ces and index. ~SBN 3-540-60451-0 (alk. paper) 1. Constructlbility (Set theory) 2. Geometry, Algebraic. I. Brecker, Ludwig, 19LiOI!. RU12, Jesus r-1. III. Title.
IV. Series. QA248.A67 1996 516' . 13--dc20
95-51853
CIP
Mathematics Subject Classification (1991): 12JXX, 13Fxx, 13JXX, 14PXX ISBN -13: 978-3-642-80026-9 e- ISBN -13: 978-3-642-80024-5 DOl: 10.1007/978-3-642-80024-5 This work is subject to copyright. All rights are reserved. whether the whole or part of the material is concerned. specifically the rights of translation. reprinting. reuse of illustrations. recitation. broadcasting. reproduction on microfilms or in any other ways. and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9. 1965. in its current version. and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. ©
Springer-Verlag Berlin Heidelberg 1996
Softcover reprint of the hardcover 1st edition 1996
SPIN 10518835
41/3143 . 5432 1 0 - Printed on acid-free paper
Preface
The plan to write this book was laid out in April 1987 at Oberwolfach, during the Conference "Reelle Algebraische Geometrie". Afterwards we met at various conferences and seminars in Luminy, Madrid, Munster, Oberwolfach, Segovia, Soesterberg, Trento and La Turballe. We would like to thank the organizers and the institutions which supported these meetings. With pleasure we remember the special year on Real Algebraic Geometry and Quadratic Forms (Ragsquad) in Berkeley 1990/91 where an essential part of this book was written. Thanks to T.Y. Lam and R. Robson. We are indepted to our Departments: Universidad Complutense de Madrid and WestfiiJische Wilhelms-Universitiit Munster, as well as the D.A.A.D. and the D.G.I.C.y'T .. It
