Search Results for "set-theory-and-the-continuum-problem-dover-books-on-mathematics"

Set Theory and the Continuum Problem

Set Theory and the Continuum Problem

  • Author: Raymond M. Smullyan,Melvin Fitting
  • Publisher: N.A
  • ISBN: 9780486474847
  • Category: Mathematics
  • Page: 315
  • View: 7031
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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

Set Theory and the Continuum Hypothesis

  • Author: Paul J. Cohen,Martin Davis
  • Publisher: Courier Corporation
  • ISBN: 0486469212
  • Category: Mathematics
  • Page: 154
  • View: 617
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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.

Zermelo's Axiom of Choice

Zermelo's Axiom of Choice

Its Origins, Development, and Influence

  • Author: Gregory H. Moore
  • Publisher: Courier Corporation
  • ISBN: 0486488411
  • Category: Mathematics
  • Page: 410
  • View: 7947
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"This book chronicles the work of mathematician Ernst Zermelo (1871-1953) and his development of set theory's crucial principle, the axiom of choice. It covers the axiom's formulation during the early 20th century, the controversy it engendered, and its current central place in set theory and mathematical logic. 1982 edition"--

Basic Set Theory

Basic Set Theory

  • Author: Azriel Levy
  • Publisher: Courier Corporation
  • ISBN: 0486150739
  • Category: Mathematics
  • Page: 416
  • View: 1361
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The first part of this advanced-level text covers pure set theory, and the second deals with applications and advanced topics (point set topology, real spaces, Boolean algebras, infinite combinatorics and large cardinals). 1979 edition.

The Axiom of Choice

The Axiom of Choice

  • Author: Thomas J. Jech
  • Publisher: N.A
  • ISBN: N.A
  • Category: Philosophy
  • Page: 202
  • View: 2594
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Continuum Mechanics

Continuum Mechanics

Concise Theory and Problems

  • Author: P. Chadwick
  • Publisher: Courier Corporation
  • ISBN: 048613914X
  • Category: Science
  • Page: 200
  • View: 2836
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DIVComprehensive treatment offers 115 solved problems and exercises to promote understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. /div

An Introduction to Stability Theory

An Introduction to Stability Theory

  • Author: Anand Pillay
  • Publisher: Courier Corporation
  • ISBN: 0486150437
  • Category: Mathematics
  • Page: 160
  • View: 2893
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This introductory treatment covers the basic concepts and machinery of stability theory. Full of examples, theorems, propositions, and problems, it is suitable for graduate students, professional mathematicians, and computer scientists. 1983 edition.

Undecidable Theories

Undecidable Theories

  • Author: Alfred Tarski,Andrzej Mostowski,Raphael Mitchel Robinson
  • Publisher: Elsevier
  • ISBN: 0444533788
  • Category: Decidability (Mathematical logic)
  • Page: 98
  • View: 9906
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Models and Ultraproducts

Models and Ultraproducts

An Introduction

  • Author: John Lane Bell,A. B. Slomson
  • Publisher: Courier Corporation
  • ISBN: 0486449793
  • Category: Mathematics
  • Page: 322
  • View: 6674
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In this text for first-year graduate students, the authors provide an elementary exposition of some of the basic concepts of model theory--focusing particularly on the ultraproduct construction and the areas in which it is most useful. The book, which assumes only that its readers are acquainted with the rudiments of set theory, starts by developing the notions of Boolean algebra, propositional calculus, and predicate calculus. Model theory proper begins in the fourth chapter, followed by an introduction to ultraproduct construction, which includes a detailed look at its theoretic properties. An overview of elementary equivalence provides algebraic descriptions of the elementary classes. Discussions of completeness follow, along with surveys of the work of Jónsson and of Morley and Vaught on homogeneous universal models, and the results of Keisler in connection with the notion of a saturated structure. Additional topics include classical results of Gödel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text.

First-order Logic

First-order Logic

  • Author: Raymond M. Smullyan
  • Publisher: Courier Corporation
  • ISBN: 9780486683706
  • Category: Mathematics
  • Page: 158
  • View: 8877
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Considered the best book in the field, this completely self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus in on the tableau point of view. Topics include trees, tableau method for propositional logic, Gentzen systems, more. Includes 144 illustrations.

The Philosophy of Set Theory

The Philosophy of Set Theory

An Historical Introduction to Cantor's Paradise

  • Author: Mary Tiles
  • Publisher: Courier Corporation
  • ISBN: 0486138550
  • Category: Mathematics
  • Page: 256
  • View: 7851
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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

Recursion Theory for Metamathematics

Recursion Theory for Metamathematics

  • Author: Raymond M. Smullyan
  • Publisher: Oxford University Press
  • ISBN: 9780195344813
  • Category: Mathematics
  • Page: 184
  • View: 9360
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This work is a sequel to the author's G?del's Incompleteness Theorems, though it can be read independently by anyone familiar with G?del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.

Forcing for Mathematicians

Forcing for Mathematicians

  • Author: Nik Weaver
  • Publisher: World Scientific
  • ISBN: 9814566020
  • Category: Mathematics
  • Page: 152
  • View: 8783
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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. Contents:Peano ArithmeticZermelo–Fraenkel Set TheoryWell-Ordered SetsOrdinalsCardinalsRelativizationReflectionForcing NotionsGeneric ExtensionsForcing EqualityThe Fundamental TheoremForcing CHForcing ¬ CHFamilies of Entire Functions*Self-Homeomorphisms of βℕ \ ℕ, I*Pure States on B(H)*The Diamond PrincipleSuslin's Problem, I*Naimark's problem*A Stronger DiamondWhitehead's Problem, I*Iterated ForcingMartin's AxiomSuslin's Problem, II*Whitehead's Problem, II*The Open Coloring AxiomSelf-Homeomorphisms of βℕ \ ℕ, II*Automorphisms of the Calkin Algebra, I*Automorphisms of the Calkin Algebra, II*The Multiverse Interpretation Readership: Graduates and researchers in logic and set theory, general mathematical audience. Keywords:Forcing;Set Theory;Consistency;Independence;C*-AlgebraKey Features:A number of features combine to make this thorough and rigorous treatment of forcing surprisingly easy to follow. First, it goes straight into the core material on forcing, avoiding Godel constructibility altogether; second, key definitions are simplified, allowing for a less technical development; and third, further care is given to the treatment of metatheoretic issuesEach chapter is limited to four pages, making the presentation very readableA unique feature of the book is its emphasis on applications to problems outside of set theory. Much of this material is currently only available in the primary literatureThe author is a pioneer in the application of set-theoretic methods to C*-algebra, having solved (together with various co-authors) Dixmier's “prime versus primitive” problem, Naimark's problem, Anderson's conjecture about pure states on B(H), and the Calkin algebra outer automorphism problemReviews: “The author presents the basics of the theory of forcing in a clear and stringent way by emphasizing important technical details and simplifying some definitions and arguments. Moreover, he presents the content in a way that should help beginners to understand the central concepts and avoid common mistakes.” Zentralblatt MATH

A Book of Set Theory

A Book of Set Theory

  • Author: Charles C Pinter
  • Publisher: Courier Corporation
  • ISBN: 0486497089
  • Category: Mathematics
  • Page: 256
  • View: 9198
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"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"--

Incompleteness in the Land of Sets

Incompleteness in the Land of Sets

  • Author: Melvin Fitting
  • Publisher: N.A
  • ISBN: 9781904987345
  • Category: Mathematics
  • Page: 142
  • View: 3236
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Russell's paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit. Logical formulas define sets (in a standard model). Formulas, being mathematical objects, can be thought of as sets themselves-mathematics reduces to set theory. Consider those formulas that do not belong to the set they define. The collection of such formulas is not definable by a formula, by the same argument that Russell used. This quickly gives Tarski's result on the undefinability of truth. Variations on the same idea yield the famous results of Godel, Church, Rosser, and Post. This book gives a full presentation of the basic incompleteness and undecidability theorems of mathematical logic in the framework of set theory. Corresponding results for arithmetic follow easily, and are also given. Godel numbering is generally avoided, except when an explicit connection is made between set theory and arithmetic. The book assumes little technical background from the reader. One needs mathematical ability, a general familiarity with formal logic, and an understanding of the completeness theorem, though not its proof. All else is developed and formally proved, from Tarski's Theorem to Godel's Second Incompleteness Theorem. Exercises are scattered throughout.

Naive Set Theory

Naive Set Theory

  • Author: Paul R. Halmos
  • Publisher: Courier Dover Publications
  • ISBN: 0486814874
  • Category: Mathematics
  • Page: 112
  • View: 8467
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Classic by prominent mathematician offers a concise introduction to set theory using language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, more. 1960 edition.

Philosophical Introduction to Set Theory

Philosophical Introduction to Set Theory

  • Author: Stephen Pollard
  • Publisher: Courier Dover Publications
  • ISBN: 0486797147
  • Category: Mathematics
  • Page: 192
  • View: 4984
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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.

Set Theory and Logic

Set Theory and Logic

  • Author: Robert R. Stoll
  • Publisher: Courier Corporation
  • ISBN: 0486139646
  • Category: Mathematics
  • Page: 512
  • View: 2984
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Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.

Diagonalization and Self-reference

Diagonalization and Self-reference

  • Author: Raymond M. Smullyan
  • Publisher: Oxford University Press on Demand
  • ISBN: 9780198534501
  • Category: Mathematics
  • Page: 396
  • View: 8660
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The main purpose of this book is to present a unified treatment of fixed points as they occur in Godel's incompleteness proofs, recursion theory, combinatory logic, semantics and metamathematics. It provides a survey of introductory material and a summary of recent research. The first chapters are of an introductory nature, and consist mainly of exercises with solutions given to most of them. The book should be of interest to researchers and graduate students in mathematical logic.

Contributions to the Founding of the Theory of Transfinite Numbers

Contributions to the Founding of the Theory of Transfinite Numbers

  • Author: Georg Cantor
  • Publisher: N.A
  • ISBN: N.A
  • Category: Number theory
  • Page: 211
  • View: 4784
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