First Order Categorical Logic Model-Theoretical Methods in the Theor
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611 Michael Makkai Gonzalo E. Reyes
First Order Categorical Logic Model-Theoretical Methods in the Theory of Topoi and Related Categories
Springer-Verlag Berlin Heidelberg NewYork 1977
Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann
611 Michael Makkai Gonzalo E. Reyes
First Order Categorical Logic Model-Theoretical Methods in the Theory of Topoi and Related Categories
Springer-Verlag Berlin Heidelberg NewYork 1977
Authors Michael Makkai Department of Mathematics McGill University Burnside Hall 805 Sherbrooke Street West Montreal PO Canada H3A 2K6 Gonzalo E. Reyes Department of Mathematics Universite de Montreal Montreal, PO, Canada
Library of Congress Cataloging in Publication Data
Makkai, Michael, 1939First order catetgorical logic. (Lecture notes in mat.hematrLca ; 611) Bibliography: p , 1. Model theory. 2. Categories (Mathematics) 3. Toposes. I. Reyes, Gonzalo, 1937joint author. II. Title. III. Series: Lecture notes in mathematics (Berlin ) ; 611. QA3.L28 no. 611 [QA9.7J 510' .8s [512'.55J 71-13221
AMS Subject Classifications (1970): 02H05, 02Hl0, 02J99, 14F20, 18Fl0,18F20 ISBN 3-540-08439-8 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-08439-8 Springer-Verlag New York Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
TO ZSUZSI AND MARIE
PREFACE
We arrived at the idea of writing a book on the connections of first order model theory and categories in early 1974 when we realized that it was impossible to communicate some of our fresh results and proofs because of the lack of a basic theory and a coherent terminology connecting logic and categories.
As expected in such cases, it has
taken us longer than promised to many people to complete the arduous task of writing this book. The basic features of the work, some of them unusual, will be described in the Introduction below; Primar
here we make a few remarks only.
,the book is intended as a research monograph contain-
ing the exposition of the authors' results.
On the other hand, it
resembles a textbook because of the large amount of basic, sometimes even wellknown, material that we have included. book is an essentially selfcontained reading.
As a result, the
However, the reader
should be warnep that we have made no attempt to give a complete or even balanced account of the subj ect matter on the whole and it would be misleading to take the book as a faithful representation of the whole of categorical logic. Our ideal goal in offering this w
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