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Author : Arthur H. Kruse
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.:/5 (41 download)
Download or read book Localization and Iteration of Axiomatic Set Theory written by Arthur H. Kruse and published by . This book was released on 1969 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Arthur H. Kruse
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (844 download)
Download or read book Localization and iteration of axiomatic set theory written by Arthur H. Kruse and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 0080957412
Total Pages : 235 pages
Book Rating : 4.0/5 (89 download)
Download or read book Axiomatic Set Theory written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Axiomatic Set Theory
Author : Kazimierz Kuratowski
Publisher : Elsevier
ISBN 13 : 1483151638
Total Pages : 353 pages
Book Rating : 4.4/5 (831 download)
Download or read book Introduction to Set Theory and Topology written by Kazimierz Kuratowski and published by Elsevier. This book was released on 2014-07-10 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.
Author : Thomas J. Jech
Publisher : American Mathematical Soc.
ISBN 13 : 0821802461
Total Pages : 232 pages
Book Rating : 4.8/5 (218 download)
Download or read book Axiomatic Set Theory, Part 2 written by Thomas J. Jech and published by American Mathematical Soc.. This book was released on 1971 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R.B. Chuaqui
Publisher : Newnes
ISBN 13 : 0080871623
Total Pages : 405 pages
Book Rating : 4.0/5 (88 download)
Download or read book Axiomatic Set Theory written by R.B. Chuaqui and published by Newnes. This book was released on 2011-08-30 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Axiomatic Set Theory
Author : Patrick Suppes
Publisher : Courier Corporation
ISBN 13 : 0486136876
Total Pages : 290 pages
Book Rating : 4.4/5 (861 download)
Download or read book Axiomatic Set Theory written by Patrick Suppes and published by Courier Corporation. This book was released on 2012-05-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : W. Hodges
Publisher : Springer
ISBN 13 : 3540371621
Total Pages : 363 pages
Book Rating : 4.5/5 (43 download)
Download or read book Conference in Mathematical Logic - London '70 written by W. Hodges and published by Springer. This book was released on 2006-11-15 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J.L. Krivine
Publisher : Springer Science & Business Media
ISBN 13 : 9401031444
Total Pages : 108 pages
Book Rating : 4.4/5 (1 download)
Download or read book Introduction to Axiomatic Set Theory written by J.L. Krivine and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Author : James E. Baumgartner
Publisher :
ISBN 13 :
Total Pages : 282 pages
Book Rating : 4.X/5 (4 download)
Download or read book Axiomatic Set Theory written by James E. Baumgartner and published by . This book was released on 1984 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Edward John Lemmon
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.:/5 (42 download)
Download or read book Introduction to Axiomatic Set Theory written by Edward John Lemmon and published by . This book was released on 1969 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Arthur Knoebel
Publisher : Springer Science & Business Media
ISBN 13 : 0817646426
Total Pages : 336 pages
Book Rating : 4.8/5 (176 download)
Download or read book Sheaves of Algebras over Boolean Spaces written by Arthur Knoebel and published by Springer Science & Business Media. This book was released on 2011-12-16 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique monograph building bridges among a number of different areas of mathematics such as algebra, topology, and category theory. The author uses various tools to develop new applications of classical concepts. Detailed proofs are given for all major theorems, about half of which are completely new. Sheaves of Algebras over Boolean Spaces will take readers on a journey through sheaf theory, an important part of universal algebra. This excellent reference text is suitable for graduate students, researchers, and those who wish to learn about sheaves of algebras.
Author : Stephen Pollard
Publisher : Courier Dover Publications
ISBN 13 : 0486797147
Total Pages : 196 pages
Book Rating : 4.4/5 (867 download)
Download or read book Philosophical Introduction to Set Theory written by Stephen Pollard and published by Courier Dover Publications. This book was released on 2015-07-15 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
Author : José Ferreirós
Publisher : Springer Science & Business Media
ISBN 13 : 376438350X
Total Pages : 486 pages
Book Rating : 4.7/5 (643 download)
Download or read book Labyrinth of Thought written by José Ferreirós and published by Springer Science & Business Media. This book was released on 2008-10-04 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: "José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century." --Bulletin of Symbolic Logic (Review of first edition)
Author : G. Takeuti
Publisher : Springer Science & Business Media
ISBN 13 : 1468487515
Total Pages : 244 pages
Book Rating : 4.4/5 (684 download)
Download or read book Axiomatic Set Theory written by G. Takeuti and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Yiannis Moschovakis
Publisher : Springer Science & Business Media
ISBN 13 : 9780387941806
Total Pages : 296 pages
Book Rating : 4.9/5 (418 download)
Download or read book Notes on Set Theory written by Yiannis Moschovakis and published by Springer Science & Business Media. This book was released on 1994-02-18 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.
Author : G. Takeuti
Publisher : Springer Science & Business Media
ISBN 13 : 1468499157
Total Pages : 255 pages
Book Rating : 4.4/5 (684 download)
Download or read book Introduction to Axiomatic Set Theory written by G. Takeuti and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1963, the first author introduced a course in set theory at the Uni versity of Illinois whose main objectives were to cover G6del's work on the consistency of the axiom of choice (AC) and the generalized con tinuum hypothesis (GCH), and Cohen's work on the independence of AC and the GCH. Notes taken in 1963 by the second author were the taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are highlighted, and second, the student who wishes to master the sub ject is compelled to develop the details on his own. However, an in structor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text. We have chosen instead a development that is quite detailed and complete. For our slow development we claim the following advantages. The text is one from which a student can learn with little supervision and instruction. This enables the instructor to use class time for the presentation of alternative developments and supplementary material.
