Infinitary Combinatorics and the Axiom of Determinateness
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612 Eugene M. Kleinberg
Infinitary Combinatorics and the Axiom of Determinateness
SpringerVeriag Berlin Heidelberg New York 1977
Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann Subseries: Harvard/MIT Adviser: G. Sacks
612 Eugene M. Kleinberg
Infinitary Combinatorics and the Axiom of Determinateness
SpringerVeriag Berlin Heidelberg New York 1977
Author Eugene M. Kleinberg Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139/USA
AMS Subject Classifications (1970): 02-02,02 K15,02 K35, 05A17
04 A20,
ISBN 3-540-08440-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-08440-1 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 1977 Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
For Evie
I know a reasonable woman, Handsome and witty, yet a friend. Not warped by passion, awed by rumor, Not grave through pride, or gay through folly, An equal mixture of good humor, And sensible soft melancholy. -- Alexander Pope
Acknowledgements
These notes are distilled from a number of courses I taught at M.I.T. between 1970 and 1976.
They first appeared
in draft form as material for a graduate course given here last fall. The subject matter itself was initiated mainly through the work of Martin and Solovay in the late 1960's.
lowe a
strong intellectual debt to both of them. Special credit is due to Professor J. M. Henle.
He is
a major contributor to the development of the field, and many of his results appear throughout these notes. In preparing this manuscript, I had extensive and
expert help from many of my students, most notably from Arthur Apter. Finally, lowe special thanks to Denise Borsuk for her patience, skill, and intuition in transforming my assorted notes to type.
Cambridge, Mass. 22 April 1977
Table of Contents
In traduction . . • . • . . • . • • . . . . . . . . . . . . . . . . . . . . . • . • . . . . . . . . . .
Chapter
I . . . . . . . . . .. .•....... ... .... .. .. ••.•••. ... ....
9
Chapter
I I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
22
Chapter III . . . . . • . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . .
49
Chapter
IV... . . . . . . • . . . . . . . . • . . . . . . . . . . . . . . . . . • . • . . . . ..
55
Chapter
V. . • . . • . • • . . . . . • . • . . . . . . . . . . . . . . . . . . • • • . . . . . ..
79
Chapter
VI . . . . • . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • .
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