Self-Reference and Modal Logic
It is Sunday, the 7th of September 1930. The place is Konigsberg and the occasion is a small conference on the foundations of mathematics. Arend Heyting, the foremost disciple of L. E. J. Brouwer, has spoken on intuitionism; Rudolf Carnap of the Vienna Ci
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F.W. Gehring P.R. Halmos C.C. Moore
Universitext Editors: F.W. Gehring, P.R. Halmos,
c.c.
Moore
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C. Smorynski
Self-Reference and Modal Logic
Springer-Verlag New York Berlin Heidelberg Tokyo
C. Smorynski Department of Mathematics and Computer Science San Jose State University San Jose, CA 95192 U.S.A.
AMS Subject Classification: 03-02, 03B45
Library of Congress Cataloging-in-Publication Data Smorynski, C. Self-reference and modal logic. (U niversitext) Bibliography: p. I. Modality (Logic) I. Title. 85-17219 QA9.46.S6 1985 511.3 © 1985 by Springer-Verlag New York Inc. Reprint ofthe original edition 1985 All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag, 175 Fifth Avenue, New York, New York 10010, U.S.A.
9 8 765 4 3 2 I
ISBN-13: 978-0-387-96209-2 e-ISBN-13: 978-1-4613-8601-8 DOl: 10.1007/978-1-4613-8601-8
TO
GOOD OLD HATS ON THE ONE FIXED POINT IN A CHANGING AGE
Forevvord
In the fall of 1980 I had the great pleasure of visiting the University of Warsaw at the invitation of Cecylia Rauszer and lecturing on the modal logic of provability.
When one lectures in English in a country in which English is not the
native language, one must, of course, try to remember not to get nervous and speak too rapidly, as one's hosts can often be too polite to interrupt. best strategy is to write up notes to be passed around.
In the end, the
These are not those.
Between the time of submission of my original lecture notes for the series Lecture Notes in Mathematics and Roberto Minio's suggestion of Universitext, I learned a li
