Axiomatic Set Theory Part 2
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Axiomatic Set Theory Part 2
Author | : Thomas J. Jech |
Publsiher | : American Mathematical Soc. |
Total Pages | : 232 |
Release | : 1971 |
Genre | : Axiomatic set theory |
ISBN | : 9780821802465 |
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Axiomatic Set Theory
Author | : Patrick Suppes |
Publsiher | : Courier Corporation |
Total Pages | : 265 |
Release | : 2012-05-04 |
Genre | : Mathematics |
ISBN | : 9780486136875 |
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Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
Axiomatic Set Theory
Author | : G. Takeuti,W.M. Zaring |
Publsiher | : Springer Science & Business Media |
Total Pages | : 244 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 9781468487510 |
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This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory material al1 the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained.
Introduction to Axiomatic Set Theory
Author | : J.L. Krivine |
Publsiher | : Springer Science & Business Media |
Total Pages | : 108 |
Release | : 2012-12-06 |
Genre | : Philosophy |
ISBN | : 9789401031448 |
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This book presents the classic relative consistency proofs in set theory that are obtained by the device of 'inner models'. Three examples of such models are investigated in Chapters VI, VII, and VIII; the most important of these, the class of constructible sets, leads to G6del's result that the axiom of choice and the continuum hypothesis are consistent with the rest of set theory [1]I. The text thus constitutes an introduction to the results of P. Cohen concerning the independence of these axioms [2], and to many other relative consistency proofs obtained later by Cohen's methods. Chapters I and II introduce the axioms of set theory, and develop such parts of the theory as are indispensable for every relative consistency proof; the method of recursive definition on the ordinals being an import ant case in point. Although, more or less deliberately, no proofs have been omitted, the development here will be found to require of the reader a certain facility in naive set theory and in the axiomatic method, such e as should be achieved, for example, in first year graduate work (2 cycle de mathernatiques).
Axiomatic Set Theory
Author | : Paul Bernays |
Publsiher | : Courier Dover Publications |
Total Pages | : 244 |
Release | : 1958 |
Genre | : Axiomatic set theory |
ISBN | : UCAL:B4249731 |
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Axiomatic Set Theory
Author | : R.B. Chuaqui |
Publsiher | : Newnes |
Total Pages | : 385 |
Release | : 2011-08-30 |
Genre | : Mathematics |
ISBN | : 0080871623 |
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Axiomatic Set Theory
Axiomatic Set Theory Part 1
Author | : Dana S. Scott,Thomas J. Jech |
Publsiher | : American Mathematical Soc. |
Total Pages | : 482 |
Release | : 1971-12-31 |
Genre | : Mathematics |
ISBN | : 9780821802458 |
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Set Theory
Author | : Thomas Jech |
Publsiher | : Springer |
Total Pages | : 652 |
Release | : 2014-01-15 |
Genre | : Electronic Book |
ISBN | : 3662224011 |
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This monograph covers the recent major advances in various areas of set theory. From the reviews: "One of the classical textbooks and reference books in set theory....The present Third Millennium edition...is a whole new book. In three parts the author offers us what in his view every young set theorist should learn and master....This well-written book promises to influence the next generation of set theorists, much as its predecessor has done." --MATHEMATICAL REVIEWS"