Towards an Arithmetical Logic The Arithmetical Foundations of Logic
This book offers an original contribution to the foundations of logic and mathematics, and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the
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Yvon Gauthier
Towards an Arithmetical Logic The Arithmetical Foundations of Logic
Studies in Universal Logic Series Editor Jean-Yves Béziau (Federal University of Rio de Janeiro and Brazilian Research Council, Rio de Janeiro, Brazil) Editorial Board Members Hajnal Andréka (Hungarian Academy of Sciences, Budapest, Hungary) Mark Burgin (University of California, Los Angeles, USA) Razvan Diaconescu (Romanian Academy, Bucharest, Romania) Josep Maria Font (University of Barcelona, Spain) Andreas Herzig (Centre National de la Recherche Scientifique, Toulouse, France) Arnold Koslow (City University of New York, USA) Jui-Lin Lee (National Formosa University, Huwei Township, Taiwan) Larissa Maksimova (Russian Academy of Sciences, Novosibirsk, Russia) Grzegorz Malinowski (University of Łód´z, Poland) Darko Sarenac (Colorado State University, Fort Collins, USA) Peter Schröder-Heister (University Tübingen, Germany) Vladimir Vasyukov (Russian Academy of Sciences, Moscow, Russia)
This series is devoted to the universal approach to logic and the development of a general theory of logics. It covers topics such as global set-ups for fundamental theorems of logic and frameworks for the study of logics, in particular logical matrices, Kripke structures, combination of logics, categorical logic, abstract proof theory, consequence operators, and algebraic logic. It includes also books with historical and philosophical discussions about the nature and scope of logic. Three types of books will appear in the series: graduate textbooks, research monographs, and volumes with contributed papers. More information about this series at http://www.springer.com/series/7391
Yvon Gauthier
Towards an Arithmetical Logic The Arithmetical Foundations of Logic
Yvon Gauthier University of Montreal Montreal Québec, Canada
ISSN 2297-0282 Studies in Universal Logic ISBN 978-3-319-22086-4 DOI 10.1007/978-3-319-22087-1
ISSN 2297-0290
(electronic)
ISBN 978-3-319-22087-1
(eBook)
Library of Congress Control Number: 2015949819 Mathematics Subject Classification (2010): 01-02, 03-02, 03-A05, 13F-20, 14-02 Springer Cham Heidelberg New York Dordrecht London © 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are be
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