Forcing, Arithmetic, Division Rings
- PDF / 10,387,129 Bytes
- 257 Pages / 609.45 x 790.87 pts Page_size
- 8 Downloads / 212 Views
454 Joram Hirschfeld William H. Wheeler
Forcing, Arithmetic, Division Rings
Springer-Verlag Berlin· Heidelberg· New York 1975
Authors Dr. Joram Hirschfeld Department of Mathematics Tel Aviv University Ramat Aviv Tel Aviv Israel Dr. William H. Wheeler Bedford College University of London London England Permanent address: Department of Mathematics Indiana University Bloomington, Indiana 47401 USA
Library of Congress Cataloging in Publication Data
Hirschfeld, Joram.
Forcing, arithmetic, and division rings. (Lecture notes in mathematics ; 454)
Bibliography: p.
Includes index.
1. Forcing (Model theory) 2. Model theory.
3. Division rings. I. Wheeler, William H., 1946-
joint author. II. Title. III. Series: Lecture notes
in mathematics (Berlin) ; 454. QA3.L28 no. 454 [QA9.7] 510'.8 [511'.8] 75-12981
AMS Subject Classifications (1970): 02 H05, 02 H13, 02 H15, 02 H20 08 A20, 10 N10, 10 N15, 16 A40 ISBN 3-540-07157-1 Springer-Verlag Berlin · Heidelberg · New York ISBN 0-387-07157-1 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 1975. Printed in Germany.
Offsetdruck: Julius Beltz, Hemsbach/Bergstr.
In memory of Abraham Robinson
ACKNOWLEDGEMENTS
We gratefully acknowledge the contributions of our colleagues and coworkers to this volume.
Deserving of special mention are
Mrs. S. Mandel for typing Part Two; L. Manevitz, D. Saracino, P. van Praag, and P. M. Cohn for their valuable comments and criticism of the manuscript; the members of the 1973-1974 Bedford College (University of London) logic seminar, to whom much of the material herein was presented, for their questions and comments; and the members of the Department of Mathematics of Yale University, 1969-1972, especially N. Jacobson, J. Barwise, G. Sacks, E. Fisher, M. Lerman, J. Schmerl, and S. Simpson, for their instruction and suggestions. We are indebted especially to Abraham Robinson, our adviser, for his guidance and encouragement and for the proposal of this volume. Finally, we thank our wives for their patience and moral support during the writing and preparation of this volume; the second author acknowledges in particular his gratitude to his wife for her labor of love in typing Parts One and Three.
Joram Hirschfeld William H. Wheeler
CONTENTS
INTRODUCTION
1
11
PART ONE FORCING CHAPTER
1
CHAPTER
2
CHAPTER
3
X
EXISTENTIALLY COMPLETE STRUCTURES AND EXISTENTIALLY UNIVERSAL STRUCTURES Existentially Complete Structures § 1 § 2 Existential Types and Existentially Universal Structures
)( MODEL-COMPLETIONS AND MODEL-COMPANIONS
Data Loading...
