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CB481-Tourlakis CB481-FMDrv September 4, 2002 14:14 Char Count= 0
LECTURES IN LOGIC
AND SET THEORY
Volume 1: Mathematical Logic
E TOURLAKIS
York University
iii
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published by the press syndicate of the university of cambridge
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
cambridge university press
The Edinburgh Building, Cambridge CB2 2RU, UK
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
Ruiz de Alarcon´ 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
C e Tourlakis 2003
This book is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published 2003
Printed in the United Kingdom at the University Press, Cambridge
Typeface Times 10/13 pt. System LATEX2ε[tb]
A catalog record for this book is available from the British Library.
Library of Congress Cataloging in Publication Data
Tourlakis, e J.
Lectures in logic and set theory / e Tourlakis.
p. cm. –(Cambridge studies in advanced mathematics)
Includes bibliographical references and index.
Contents: v. 1. Mathematical logic – v. 2. Set theory.
ISBN 0-521-75373-2 (v. 1) – ISBN 0-521-75374-0 (v. 2)
1. Logic, Symbolic and mathematical. 2. Set theory. I. Title. II. Series.
.T68 2003
– dc21 2002073308
ISBN 0 521 75373 2 hardback
iv
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Contents
Preface page ix
I Basic Logic 1
First Order Languages 5
A Digression into the Metatheory:
Informal Induction and Recursion 19
Axioms and Rules of Inference 28
Basic Metatheorems 42
Semantics; Soundness, Completeness, Compactness 52