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Author : K. J. Devlin
Publisher : Springer
ISBN 13 : 354037034X
Total Pages : 105 pages
Book Rating : 4.45/5 ( download)
Download or read book The Axiom of Constructibility written by K. J. Devlin and published by Springer. This book was released on 2006-11-15 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : K. J. Devlin
Publisher :
ISBN 13 : 9783662204320
Total Pages : 108 pages
Book Rating : 4.20/5 ( download)
Download or read book The Axiom of Constructibility written by K. J. Devlin and published by . This book was released on 2014-09-01 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frederick Rowbottom
Publisher :
ISBN 13 :
Total Pages : 164 pages
Book Rating : 4.62/5 ( download)
Download or read book Some Strong Axioms of Infinity Incompatible with the Axiom of Constructibility written by Frederick Rowbottom and published by . This book was released on 1964 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 9780080955001
Total Pages : 634 pages
Book Rating : 4.02/5 ( download)
Download or read book Provability, Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection
Author : A.A. Fraenkel
Publisher : Elsevier
ISBN 13 : 0080887058
Total Pages : 415 pages
Book Rating : 4.50/5 ( download)
Download or read book Foundations of Set Theory written by A.A. Fraenkel and published by Elsevier. This book was released on 1973-12-01 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.
Author : Michael Potter
Publisher : Clarendon Press
ISBN 13 : 0191556432
Total Pages : 362 pages
Book Rating : 4.32/5 ( download)
Download or read book Set Theory and its Philosophy written by Michael Potter and published by Clarendon Press. This book was released on 2004-01-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Author : Keith J. Devlin
Publisher : Cambridge University Press
ISBN 13 : 1316739422
Total Pages : 439 pages
Book Rating : 4.26/5 ( download)
Download or read book Constructibility written by Keith J. Devlin and published by Cambridge University Press. This book was released on 2017-03-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the sixth publication in the Perspectives in Logic series, Keith J. Devlin gives a comprehensive account of the theory of constructible sets at an advanced level. The book provides complete coverage of the theory itself, rather than the many and diverse applications of constructibility theory, although applications are used to motivate and illustrate the theory. The book is divided into two parts: Part I (Elementary Theory) deals with the classical definition of the Lα-hierarchy of constructible sets and may be used as the basis of a graduate course on constructibility theory. and Part II (Advanced Theory) deals with the Jα-hierarchy and the Jensen 'fine-structure theory'.
Author : Azriel Levy
Publisher : Courier Corporation
ISBN 13 : 0486150739
Total Pages : 418 pages
Book Rating : 4.34/5 ( download)
Download or read book Basic Set Theory written by Azriel Levy and published by Courier Corporation. This book was released on 2012-06-11 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.
Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 331901577X
Total Pages : 253 pages
Book Rating : 4.74/5 ( download)
Download or read book The Real Numbers written by John Stillwell and published by Springer Science & Business Media. This book was released on 2013-10-16 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.
Author : C. Alkor
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.40/5 ( download)
Download or read book Constructibility in Ackermann's Set Theory written by C. Alkor and published by . This book was released on 1982 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
