A Course in Mathematical Logic for Mathematicians
A Course in Mathematical Logic for Mathematicians, Second Edition offers a straightforward introduction to modern mathematical logic that will appeal to the intuition of working mathematicians. The book begins with an elementary introduction to formal lan
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Editorial Board S. Axler K.A. Ribet
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Yu. I. Manin
A Course in Mathematical Logic for Mathematicians Second Edition
Chapters I-VIII translated from the Russian by Neal Koblitz With new chapters by Boris Zilber and Yuri I. Manin
Author: Yu. I. Manin Max-Planck Institut für Mathematik 53111 Bonn Germany [email protected]
Contributor: B. Zilber Mathematical Institute University of Oxford Oxford OX1 3LB United Kingdom [email protected]
First Edition Translated by: Neal Koblitz Department of Mathematics University of Washington Seattle, WA 98195 USA [email protected]
Editorial Board: S. Axler Mathematics Department San Francisco State University San Francisco, CA 94132 USA [email protected]
K. A. Ribet Mathematics Department University of California at Berkeley Berkeley, CA 94720 USA [email protected]
ISSN 0072-5285 ISBN 978-1-4419-0614-4 e-ISBN 978-1-4419-0615-1 DOI 10.1007/978-1-4419-0615-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009934521 Mathematics Subject Classification (2000): 03-XX, 03-01 © Second edition 2010 by Yu. I. Manin © First edition 1977 by Springer Verlag, New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Nikita, Fedor and Mitya, with love
Preface to the Second Edition
1. The first edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about infinities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decid
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