Gentzen's Centenary The Quest for Consistency
Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contribution
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Gentzen’s Centenary The Quest for Consistency
Gentzen’s Centenary
Reinhard Kahle • Michael Rathjen Editors
Gentzen’s Centenary The Quest for Consistency
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Editors Reinhard Kahle Departamento de Matemática, FCT Universidade Nova de Lisboa Lisbon Portugal
Michael Rathjen School of Mathematics University of Leeds Leeds United Kingdom
ISBN 978-3-319-10102-6 ISBN 978-3-319-10103-3 (eBook) DOI 10.1007/978-3-319-10103-3 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2015953429 Mathematics Subject Classification (2010): 03F03, 03F05, 03F15, 03F25, 03F30, 03F35, 03-03, 01A60, 03A05 © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, 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 physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Cover image: Photo is published with kind permission of © Eckart Menzler. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
With kind permission of © Eckart Menzler
This volume is a tribute by several generations of proof theorists to Gerhard Gentzen, one of the greatest logicians ever to whom we owe the most profound investigation of the nature of proofs since Aristotle and Frege. The immediate stimulus for its inception was Gentzen’s 100th birthday in 2009 which was celebrated with a conference in Leeds and a workshop in Coimbra at which most of the contributors to this volume spoke
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