Measurable Cardinals
Let S be an infinite set. A measure on S (a nontrivial Σ-additive measure, to be more precise) is a real-valued function μ on P(S) such that: $$\begin{array}{*{20}{c}} {\left( i \right)\quad \mu \left( \phi \right) = 0\,and\,\mu \left( S \right) = 1;} \hf
- PDF / 51,780,712 Bytes
- 642 Pages / 439.37 x 666.142 pts Page_size
- 9 Downloads / 170 Views
•
In
Mathematica I Log ic
Editors S. Feferman W. A. Hodges M. Lerman (Managing Editor) A. J. Macintyre M. Magidor Y. N. Moschovakis
Springer-Verlag Berlin Heidelberg GmbH
Thomas Jech
Set Theory Second Corrected Edition
Springer
Thomas Jech Department of Mathematics The Pennsylvania State University University Park, PA 16802 USA e-mail: [email protected]
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Jech, Thomas J.: Sct theory / Thomas Jech. - 2., corr. ed. - Berlin; Heidelberg; New York; Barcelona ; Budapest ; Hong Kong; London; Milan; Paris ; Santa Clara; Singapore ; Tokyo : Springer, 1997 (Perspectives in mathematical logic)
The original edition was published in 1978 by Academic Press, Inc. in the series Pure and Applied Mathematics, vol. 79. with the
Mathematics Subject Classification (1991): 03E05, 03EIO, 03E15, 03E20, 03E25, 03E30, 03E35, 03E40, 03E45, 03E47,03E50, 03E55, 03E60, 04AI0, 04A15, 04A20, 04A25, 04A30
ISSN 0172-6641 ISBN 978-3-662-22402-1
ISBN 978-3-662-22400-7 (eBook) DOI 10.1007/978-3-662-22400-7 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting. reproduction on microfilms or in any other ways. and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1997 Originally published by Springer-Verlag Berlin Heidelberg New York in 1997. Softcover reprint of the hardcover 2nd edition 1997
Typesetting: in LATEX by the author; pages 1-621 were reproduced from the original edition 4113143 - 543210 - Printed on acid-free paper SPIN 10629652
Perspectives in Mathematical Logic
This series was founded in 1969 by the Omega Group consisting of R. O. Gandy, H. Hermes, A. Levy, G. H. Muller, G. E. Sacks and D. S. Scott. Initially sponsored by a grant from the Stiftung Volkswagenwerk, the series appeared under the auspices of the Heidelberger Akademie der Wissenschaften. Since 1986, Perspectives in Mathematical Logic is published under the auspices of the Association for Symbolic Logic. Mathematical Logicis a subject which is both rich and varied. Its origins lie in philosophy and the foundations of mathematics. But during the last half century it has formed deep links with algebra, geometry, analysis and other branches of mathematics. More recently it has become a central theme in theoretical computer science, and its influence in linguistics is growing fast. The books in the series differ in level. Some are introductory texts suitable for final year undergraduate or first year graduate courses, while others are specialized monographs. Some are expositions ofwellestablished material, some
