Set Theory And The Continuum Problem

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Set Theory and the Continuum Problem

Author : Raymond M. Smullyan
Publisher :
ISBN 13 : 9780486474847
Total Pages : 0 pages
Book Rating : 4.4/5 (748 download)

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Book Synopsis Set Theory and the Continuum Problem by : Raymond M. Smullyan

Download or read book Set Theory and the Continuum Problem written by Raymond M. Smullyan and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.

Set Theory and the Continuum Hypothesis

Author : Paul J. Cohen
Publisher : Courier Corporation
ISBN 13 : 0486469212
Total Pages : 196 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Set Theory and the Continuum Hypothesis by : Paul J. Cohen

Download or read book Set Theory and the Continuum Hypothesis written by Paul J. Cohen and published by Courier Corporation. This book was released on 2008-12-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Set Theory and the Continuum Problem

Author : Raymond M. Smullyan
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Set Theory and the Continuum Problem by : Raymond M. Smullyan

Download or read book Set Theory and the Continuum Problem written by Raymond M. Smullyan and published by Oxford University Press, USA. This book was released on 1996 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set Theory and the Continuum Problem is a novel introduction to set theory, including axiomatic development, consistency, and independence results. It is self-contained and covers all the set theory that a mathematician should know. Part I introduces set theory, including basic axioms, development of the natural number system, Zorn's Lemma and other maximal principles. Part II proves the consistency of the continuum hypothesis and the axiom of choice, with material on collapsing mappings, model-theoretic results, and constructible sets. Part III presents a version of Cohen's proofs of the independence of the continuum hypothesis and the axiom of choice. It also presents, for the first time in a textbook, the double induction and superinduction principles, and Cowen's theorem. The book will interest students and researchers in logic and set theory.

Set Theory and its Philosophy

Author : Michael Potter
Publisher : Clarendon Press
ISBN 13 : 0191556432
Total Pages : 362 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Set Theory and its Philosophy by : Michael Potter

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.

An Introduction to Homological Algebra

Author : Charles A. Weibel
Publisher : Cambridge University Press
ISBN 13 : 113964307X
Total Pages : 470 pages
Book Rating : 4.1/5 (396 download)

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Book Synopsis An Introduction to Homological Algebra by : Charles A. Weibel

Download or read book An Introduction to Homological Algebra written by Charles A. Weibel and published by Cambridge University Press. This book was released on 1995-10-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.

Labyrinth of Thought

Author : Jose Ferreiros
Publisher : Springer Science & Business Media
ISBN 13 : 9783764357498
Total Pages : 472 pages
Book Rating : 4.3/5 (574 download)

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Book Synopsis Labyrinth of Thought by : Jose Ferreiros

Download or read book Labyrinth of Thought written by Jose Ferreiros and published by Springer Science & Business Media. This book was released on 2001-11-01 with total page 472 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. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

Classic Set Theory

Author : D.C. Goldrei
Publisher : Routledge
ISBN 13 : 1351460609
Total Pages : 300 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Classic Set Theory by : D.C. Goldrei

Download or read book Classic Set Theory written by D.C. Goldrei and published by Routledge. This book was released on 2017-09-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

A Book of Set Theory

Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486497089
Total Pages : 259 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Book of Set Theory by : Charles C Pinter

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"--

Problems and Theorems in Classical Set Theory

Author : Peter Komjath
Publisher : Springer Science & Business Media
ISBN 13 : 0387362193
Total Pages : 492 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Problems and Theorems in Classical Set Theory by : Peter Komjath

Download or read book Problems and Theorems in Classical Set Theory written by Peter Komjath and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.

Notes on Set Theory

Author : Yiannis Moschovakis
Publisher : Springer Science & Business Media
ISBN 13 : 1475741537
Total Pages : 280 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Notes on Set Theory by : Yiannis Moschovakis

Download or read book Notes on Set Theory written by Yiannis Moschovakis and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 280 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.

Combinatorial Set Theory

Author : Lorenz J. Halbeisen
Publisher : Springer
ISBN 13 : 3319602314
Total Pages : 586 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Combinatorial Set Theory by : Lorenz J. Halbeisen

Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer. This book was released on 2017-12-20 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.

Set Theory of the Continuum

Author : Haim Judah
Publisher : Springer Science & Business Media
ISBN 13 : 1461397545
Total Pages : 417 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Set Theory of the Continuum by : Haim Judah

Download or read book Set Theory of the Continuum written by Haim Judah and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin.

Set Theory and Metric Spaces

Author : Irving Kaplansky
Publisher : American Mathematical Society
ISBN 13 : 1470463849
Total Pages : 140 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Set Theory and Metric Spaces by : Irving Kaplansky

Download or read book Set Theory and Metric Spaces written by Irving Kaplansky and published by American Mathematical Society. This book was released on 2020-09-10 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book that could profitably be read by many graduate students or by seniors in strong major programs … has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. … There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem … The presentation of metric spaces before topological spaces … should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar. —Canadian Mathematical Bulletin Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent. — Lance Small, UC San Diego This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.

The Axiom of Choice

Author : Thomas J. Jech
Publisher : Courier Corporation
ISBN 13 : 0486466248
Total Pages : 226 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis The Axiom of Choice by : Thomas J. Jech

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.

The Philosophy of Set Theory

Author : Mary Tiles
Publisher : Courier Corporation
ISBN 13 : 0486138550
Total Pages : 258 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis The Philosophy of Set Theory by : Mary Tiles

Download or read book The Philosophy of Set Theory written by Mary Tiles and published by Courier Corporation. This book was released on 2012-03-08 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div

Interpreting Godel

Author : Juliette Kennedy
Publisher : Cambridge University Press
ISBN 13 : 1107002664
Total Pages : 293 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Interpreting Godel by : Juliette Kennedy

Download or read book Interpreting Godel written by Juliette Kennedy and published by Cambridge University Press. This book was released on 2014-08-21 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this groundbreaking volume, leading philosophers and mathematicians explore Kurt Gödel's work on the foundations and philosophy of mathematics.

Handbook of Set Theory

Author : Matthew Foreman
Publisher : Springer Science & Business Media
ISBN 13 : 1402057644
Total Pages : 2200 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Set Theory by : Matthew Foreman

Download or read book Handbook of Set Theory written by Matthew Foreman and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 2200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.