Set Theory and Model Theory Proceedings of an Informal Symposium Hel
- PDF / 8,734,838 Bytes
- 181 Pages / 461 x 684 pts Page_size
- 91 Downloads / 173 Views
872 Set Theory and Model Theory Proceedings of an Informal Symposium Held at Bonn, June 1-3, 1979
Edited by R. B. Jensen and A. Prestel
Springer-Verlag Berlin Heidelberg New York 1981
Editors
Ronald Bjorn Jensen All Souls College Oxford OX1 4AL, England Alexander Prestel Fakultat fOr Mathematik, Universitat Konstanz Postfach 5560, 7750 Konstanz, Federal Republic of Germany
AMS Subject Classifications (1980): 03Cxx, 03Exx ISBN 3-540-10849-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-10849-1 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 "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1981 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
FOREWORD On the occasion of Gisbert Hasenjaeger's 60-th birthday an informal symposium on set theory and model theory was held at Bonn from 1.-3. of June 1979. The papers published in these proceedings are all dedicated to Professor Hasenjaeger. Since the meeting took place some of the papers have been revised and extended. All of the contributors to this volume are former students or co-workers of Professor Hasenjaeger. Each was at one time or another his assistant. Each of us, in his own approach to mathematics, bears deep traces of Hasenjaeger's influence. Hasenjaeger himself is an eager proponent of the platonic view advocated by his teacher, Heinrich Scholz. Though not all of us would call ourselves platonists today, we retain a profound sense that mathematics must have a 'real content' - and that a problem should be judged by its content, rather than its difficulty or esthetic value. All of us learned from Hasenjaeger to regard the concept of model as central in logic - a conviction to which this book bears witness. The preponderance of set theoretical contributions to this volume is related directly to Hasenjaeger's insistence on the importance of ontological questions. We fear, however, that Hasenjaeger, were he not too polite to do so, would accuse the set theorists among us of 'taking the easy road'. He recognizes the primacy of the natural numbers and feels that a major mathematical direction should be able to shed light on them. In particular, he has faith that the tools of logic will some day prove the elementary undecidability of some of the great unsolved questions of number theory (and in the process perhaps even point the way to their solution in some stronger theory). For this reason he has made a lifelong study
of non-standard models and encouraged those around
him to work on them. Some of us tried, but all eventually turned to fields with more immediate rewards. Recently, however, the
Data Loading...
