文档介绍：An Introduction to G¨odel’s Theorems
In 1931, the young Kurt G¨odelpublished his First pleteness Theorem,
which tells us that, for any sufficiently rich theory of arithmetic, there are some
arithmetical truths the theory cannot prove. This remarkable result is among
the most intriguing (and most misunderstood) in logic. G¨odel also outlined an
equally significant Second pleteness Theorem. How are these Theorems
established, and why do they matter? Peter Smith answers these questions by
presenting an unusual variety of proofs for the First Theorem, showing how to
prove the Second Theorem, and exploring a family of related results (including
some not easily available elsewhere). The formal explanations are interwoven
with discussions of the wider significance of the two Theorems. This book will
be accessible to philosophy students with a limited formal background. It is
equally suitable for mathematics students taking a first course in mathematical
logic.
Peter Smith is Lecturer in Philosophy at the University of Cambridge. His
books include Explaining Chaos (1998) and An Introduction to Formal Logic
(2003), and he is a former editor of the journal of Analysis.
An Introduction to
G¨odel’sTheorems
Peter Smith
University of Cambridge
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
Information on this title: 0521857840
© Peter Smith 2007
This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2007
ISBN-13 978-0-511-35096-2 eBook (MyiLibrary)
ISBN-10 0-511-35096-1 eBook (MyiLibrary)
ISBN-13 978-0-521-85784-0 hardback
ISBN-10 0-5