Aspects of Constructibility
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354 Keith J. Devlin University of Oslo, Oslo/Norway
Aspects of Co n stru cti b il ity
Springer-Verlag Berlin. Heidelberg • New York 1 973
A M S S u b j e c t C l a s s i f i c a t i o n s ( 1 9 7 0 ) : 02-01, 02-02, 02 K 99, 02 H 13
I S B N 3-540-06522-9 S p r i n g e r - V e r l a g B e r l i n • H e i d e l b e r g • N e w Y o r k I S B N 0-387-06522-9 S p r i n g e r - V e r l a g N e w Y o r k - H e i d e l b e r g • B e r l i n
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 1973. Library of Congress Catalog Card Number 73-15453. Printed in Germany. Offsetdruck: Julius Beltz, Hemsbach/Bergstr.
PREFACE
This set of notes is essentially eonstructibility
theory.
a first draft of a proposed book on
As such it is probably more polished
notes" but lacking the finish of a true "textbook". should publish
this draft for two reasons.
for improvements
and enlargements
this way we publish something , whereas
It seemed desirable
Firstly, by exposing
general view, we hope to gain some reader-feedback suggestions
than a mere "set of that we
the material
in the form of corrections
(or otherwise).
Secondly,
the extra work required to produce a text of of the
for such an undertaking.
Basically, information
and/or
at least
reasonable quality might well take up several years due to the limitations time available
to
the book sets out to collect together most of the existing
on constructibility,
first draft, it is inevitable
much of which is fairly recent.
However, being a
that there will be several omissions.
(For example,
it
occurred to us after the manuscript was typed that we had not included the Levy absoluteness
theorem,
although the closely related Shoenfield
absoluteness
theorem
does in fact appear.) At the other end of the scale, we have included here some results which, because of their very detailed and technical nature, will most likely not appear in any future revision of these notes. forms of Kurepa's hypothesis,
(For example, we include here very general
involving pairs of cardinals,
forms would probably be more suited to a "graduate Nevertheless, pleased to hear),
Department
May 1973.
the book as it stands will be of some value.
of Manchester,
England.
the simplest
text".)
we hope that despite its many shortcomings
of Mathematics,
The University Manchester,
whereas
(of which we shall be
ACKNOWLEDGEMENTS
It is doubtful whether we would ever have come to write this book had it not been for the kind invitation
of Professor J°E. Fenstad to spend the Autumn of 1973
at the University of Oslo, N
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