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Author : K. J. Devlin
Publisher : Springer
ISBN 13 : 354037034X
Total Pages : 105 pages
Book Rating : 4.5/5 (43 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 : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 0080955002
Total Pages : 684 pages
Book Rating : 4.0/5 (89 download)
Download or read book Foundational Studies Selected Works written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundational Studies Selected Works
Author : Keith J. Devlin
Publisher : Cambridge University Press
ISBN 13 : 110716835X
Total Pages : 438 pages
Book Rating : 4.1/5 (71 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 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.
Author : John B. Bacon
Publisher : Routledge
ISBN 13 : 1134970978
Total Pages : 125 pages
Book Rating : 4.1/5 (349 download)
Download or read book Logic from A to Z written by John B. Bacon and published by Routledge. This book was released on 2013-09-05 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy. Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics. Over 500 entries include key terms found in the study of: * Logic: Argument, Turing Machine, Variable * Set and model theory: Isomorphism, Function * Computability theory: Algorithm, Turing Machine * Plus a table of logical symbols. Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.
Author : P.C. Eklof
Publisher : Elsevier
ISBN 13 : 0080527051
Total Pages : 620 pages
Book Rating : 4.0/5 (85 download)
Download or read book Almost Free Modules written by P.C. Eklof and published by Elsevier. This book was released on 2002-04-29 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work.
Author : Thomas Bedürftig
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110468336
Total Pages : 476 pages
Book Rating : 4.1/5 (14 download)
Download or read book Philosophy of Mathematics written by Thomas Bedürftig and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-10-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection
Author : Karel Hrbacek
Publisher : CRC Press
ISBN 13 : 1482276852
Total Pages : 310 pages
Book Rating : 4.4/5 (822 download)
Download or read book Introduction to Set Theory, Revised and Expanded written by Karel Hrbacek and published by CRC Press. This book was released on 2017-12-19 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.
Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 0080957455
Total Pages : 781 pages
Book Rating : 4.0/5 (89 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 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection
Author : Joseph R. Shoenfield
Publisher : CRC Press
ISBN 13 : 135143330X
Total Pages : 351 pages
Book Rating : 4.3/5 (514 download)
Download or read book Mathematical Logic written by Joseph R. Shoenfield and published by CRC Press. This book was released on 2018-05-02 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.
Author : Keith Devlin
Publisher : Springer Science & Business Media
ISBN 13 : 146120903X
Total Pages : 204 pages
Book Rating : 4.4/5 (612 download)
Download or read book The Joy of Sets written by Keith Devlin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.
Author : Burhanuddin Baki
Publisher : Bloomsbury Publishing
ISBN 13 : 1472578716
Total Pages : 283 pages
Book Rating : 4.4/5 (725 download)
Download or read book Badiou's Being and Event and the Mathematics of Set Theory written by Burhanuddin Baki and published by Bloomsbury Publishing. This book was released on 2014-11-20 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alain Badiou's Being and Event continues to impact philosophical investigations into the question of Being. By exploring the central role set theory plays in this influential work, Burhanuddin Baki presents the first extended study of Badiou's use of mathematics in Being and Event. Adopting a clear, straightforward approach, Baki gathers together and explains the technical details of the relevant high-level mathematics in Being and Event. He examines Badiou's philosophical framework in close detail, showing exactly how it is 'conditioned' by the technical mathematics. Clarifying the relevant details of Badiou's mathematics, Baki looks at the four core topics Badiou employs from set theory: the formal axiomatic system of ZFC; cardinal and ordinal numbers; Kurt Gödel's concept of constructability; and Cohen's technique of forcing. Baki then rebuilds Badiou's philosophical meditations in relation to their conditioning by the mathematics, paying particular attention to Cohen's forcing, which informs Badiou's analysis of the event. Providing valuable insights into Badiou's philosophy of mathematics, Badiou's Being and Event and the Mathematics of Set Theory offers an excellent commentary and a new reading of Badiou's most complex and important work.
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 : Imre Lakatos
Publisher : Elsevier
ISBN 13 : 0444534113
Total Pages : 260 pages
Book Rating : 4.4/5 (445 download)
Download or read book Problems in the Philosophy of Mathematics written by Imre Lakatos and published by Elsevier. This book was released on 1967 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Brouwer
Publisher : Elsevier
ISBN 13 : 0080957668
Total Pages : 259 pages
Book Rating : 4.0/5 (89 download)
Download or read book Problems in the Philosophy of Mathematics written by Brouwer and published by Elsevier. This book was released on 2011-10-14 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems in the Philosophy of Mathematics
Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 0080957765
Total Pages : 281 pages
Book Rating : 4.0/5 (89 download)
Download or read book Constructible Sets with Applications written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constructible Sets with Applications
Author : C.C. Chang
Publisher : Courier Corporation
ISBN 13 : 0486310957
Total Pages : 674 pages
Book Rating : 4.4/5 (863 download)
Download or read book Model Theory written by C.C. Chang and published by Courier Corporation. This book was released on 2013-10-03 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: This bestselling textbook for higher-level courses was extensively revised in 1990 to accommodate developments in model theoretic methods. Topics include models constructed from constants, ultraproducts, and saturated and special models. 1990 edition.
Author : American Mathematical Society
Publisher : American Mathematical Soc.
ISBN 13 : 9780821801673
Total Pages : 514 pages
Book Rating : 4.8/5 (16 download)
Download or read book Mathematics Into the Twenty-first Century written by American Mathematical Society and published by American Mathematical Soc.. This book was released on 1992 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the summer of 1988 in Providence, the AMS celebrated its centennial with a wide range of mathematical activities. Among those was a symposium, Mathematics into the Twenty-first Century, which brought together a number of the top research mathematicians who will likely have a significant impact on the mathematics of this century. This book contains the lectures presented by 16 of the 18 individuals who spoke during the symposium. Written by some of the major international figures in mathematical research, this group of articles covers a panorama of the vital areas of mathematics at the turn of the 21st century and gives the general mathematical reader a broad perspective on some of the major trends in research.
