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Author : John Lane Bell
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 158 pages
Book Rating : 4.:/5 (44 download)
Download or read book Boolean-valued Models and Independence Proofs in Set Theory written by John Lane Bell and published by Oxford University Press, USA. This book was released on 1977 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John L. Bell
Publisher : Oxford University Press
ISBN 13 : 0199609160
Total Pages : 214 pages
Book Rating : 4.1/5 (996 download)
Download or read book Set Theory written by John L. Bell and published by Oxford University Press. This book was released on 2011-05-05 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the third edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It covers recent developments in the field and contains numerous exercises, along with updated and increased coverage of the background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory.
Author : Nik Weaver
Publisher : World Scientific
ISBN 13 : 9814566020
Total Pages : 153 pages
Book Rating : 4.8/5 (145 download)
Download or read book Forcing For Mathematicians written by Nik Weaver and published by World Scientific. This book was released on 2014-01-24 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics.
Author : Kenneth Kunen
Publisher :
ISBN 13 : 9780720422009
Total Pages : 0 pages
Book Rating : 4.4/5 (22 download)
Download or read book Set Theory written by Kenneth Kunen and published by . This book was released on 1983 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas J. Jech
Publisher : Courier Corporation
ISBN 13 : 0486466248
Total Pages : 226 pages
Book Rating : 4.4/5 (864 download)
Download or read book The Axiom of Choice written by Thomas J. Jech and published by Courier Corporation. This book was released on 2008-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486497089
Total Pages : 259 pages
Book Rating : 4.4/5 (864 download)
Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Author : John L. Bell
Publisher :
ISBN 13 : 9781848901407
Total Pages : 132 pages
Book Rating : 4.9/5 (14 download)
Download or read book Intuitionistic Set Theory written by John L. Bell and published by . This book was released on 2014-02-28 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: While intuitionistic (or constructive) set theory IST has received a certain attention from mathematical logicians, so far as I am aware no book providing a systematic introduction to the subject has yet been published. This may be the case in part because, as a form of higher-order intuitionistic logic - the internal logic of a topos - IST has been chiefly developed in a tops-theoretic context. In particular, proofs of relative consistency with IST for mathematical assertions have been (implicitly) formulated in topos- or sheaf-theoretic terms, rather than in the framework of Heyting-algebra-valued models, the natural extension to IST of the well-known Boolean-valued models for classical set theory. In this book I offer a brief but systematic introduction to IST which develops the subject up to and including the use of Heyting-algebra-valued models in relative consistency proofs. I believe that IST, presented as it is in the familiar language of set theory, will appeal particularly to those logicians, mathematicians and philosophers who are unacquainted with the methods of topos theory.
Author : D.M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 1402030924
Total Pages : 382 pages
Book Rating : 4.4/5 (2 download)
Download or read book Handbook of Philosophical Logic written by D.M. Gabbay and published by Springer Science & Business Media. This book was released on 2005-12-15 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications
Author : W. D. Hart
Publisher : Cambridge University Press
ISBN 13 : 1139491202
Total Pages : pages
Book Rating : 4.1/5 (394 download)
Download or read book The Evolution of Logic written by W. D. Hart and published by Cambridge University Press. This book was released on 2010-08-23 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.
Author : Matteo Viale
Publisher : Springer Nature
ISBN 13 : 3031716604
Total Pages : 246 pages
Book Rating : 4.0/5 (317 download)
Download or read book The Forcing Method in Set Theory written by Matteo Viale and published by Springer Nature. This book was released on with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John L. Bell
Publisher :
ISBN 13 :
Total Pages : 126 pages
Book Rating : 4.:/5 (311 download)
Download or read book Boolean-valued Models and independence proofs in set theory written by John L. Bell and published by . This book was released on 1979 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Igorʹ Aleksandrovich Aleksandrov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821831427
Total Pages : 156 pages
Book Rating : 4.8/5 (314 download)
Download or read book Second Siberian Winter School "Algebra and Analysis" written by Igorʹ Aleksandrovich Aleksandrov and published by American Mathematical Soc.. This book was released on 1992 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the second in the series of porceedings of Soviet Regional Conferences, contains papers presented at the Second Siberian Winter School; Algebra and Analysis, held at Tomsk State University in 1989. The papers touch on a variety of topics, including Lie algebras and Lie groups, sheaves, and automorphic forms.
Author : Ieke Moerdijk
Publisher : Springer
ISBN 13 : 3319924141
Total Pages : 151 pages
Book Rating : 4.3/5 (199 download)
Download or read book Sets, Models and Proofs written by Ieke Moerdijk and published by Springer. This book was released on 2018-11-23 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.
Author : Bernd Reusch
Publisher : Springer Science & Business Media
ISBN 13 : 3540347836
Total Pages : 802 pages
Book Rating : 4.5/5 (43 download)
Download or read book Computational Intelligence, Theory and Applications written by Bernd Reusch and published by Springer Science & Business Media. This book was released on 2006-09-09 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 9th Dortmund Fuzzy Days, Dortmund, Germany, 2006. This conference has established itself as an international forum for the discussion of new results in the field of Computational Intelligence. The papers presented here, all thoroughly reviewed, are devoted to foundational and practical issues in fuzzy systems, neural networks, evolutionary algorithms, and machine learning and thus cover the whole range of computational intelligence.
Author : A.G. Kusraev
Publisher : Springer Science & Business Media
ISBN 13 : 9401144435
Total Pages : 345 pages
Book Rating : 4.4/5 (11 download)
Download or read book Boolean Valued Analysis written by A.G. Kusraev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models.
Author : Abhijit Dasgupta
Publisher : Springer Science & Business Media
ISBN 13 : 1461488540
Total Pages : 434 pages
Book Rating : 4.4/5 (614 download)
Download or read book Set Theory written by Abhijit Dasgupta and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.
Author : Michael Hallett
Publisher : Oxford University Press
ISBN 13 : 9780198532835
Total Pages : 372 pages
Book Rating : 4.5/5 (328 download)
Download or read book Cantorian Set Theory and Limitation of Size written by Michael Hallett and published by Oxford University Press. This book was released on 1986 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
