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Set Theory and the Continuum Hypothesis

Set Theory and the Continuum Hypothesis Author Paul J. Cohen
ISBN-10 9780486469218
Release 2008-12-09
Pages 154
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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.

Set Theory and the Continuum Problem

Set Theory and the Continuum Problem Author Raymond M. Smullyan
ISBN-10 0486474844
Release 2010
Pages 315
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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.

Basic Set Theory

Basic Set Theory Author Azriel Levy
ISBN-10 9780486150734
Release 2012-06-11
Pages 416
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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.

Zermelo s Axiom of Choice

Zermelo s Axiom of Choice Author Gregory H. Moore
ISBN-10 9780486488417
Release 2012-09-20
Pages 410
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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"--

The Philosophy of Set Theory

The Philosophy of Set Theory Author Mary Tiles
ISBN-10 9780486138558
Release 2012-03-08
Pages 256
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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

Axiomatic Set Theory

Axiomatic Set Theory Author Patrick Suppes
ISBN-10 9780486136875
Release 2012-05-04
Pages 265
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Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.

A Book of Set Theory

A Book of Set Theory Author Charles C Pinter
ISBN-10 9780486497082
Release 2014-07-23
Pages 256
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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"--

Models and Ultraproducts

Models and Ultraproducts Author John Lane Bell
ISBN-10 9780486449791
Release 2006
Pages 322
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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.

An Introduction to Stability Theory

An Introduction to Stability Theory Author Anand Pillay
ISBN-10 9780486150437
Release 2013-05-17
Pages 160
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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.

Philosophical Introduction to Set Theory

Philosophical Introduction to Set Theory Author Stephen Pollard
ISBN-10 9780486797144
Release 2015-07-15
Pages 192
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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.

The Axiom of Choice

The Axiom of Choice Author Thomas J. Jech
ISBN-10 CORNELL:31924000209357
Release 1973
Pages 202
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The Axiom of Choice has been writing in one form or another for most of life. You can find so many inspiration from The Axiom of Choice also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Axiom of Choice book for free.

Set Theory and its Philosophy

Set Theory and its Philosophy Author Michael Potter
ISBN-10 9780191556432
Release 2004-01-15
Pages 360
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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.

Combinatorial Set Theory

Combinatorial Set Theory Author Lorenz J. Halbeisen
ISBN-10 1447121732
Release 2011-11-24
Pages 456
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This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

Undecidable Theories

Undecidable Theories Author Alfred Tarski
ISBN-10 9780444533784
Release 1953
Pages 98
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Undecidable Theories has been writing in one form or another for most of life. You can find so many inspiration from Undecidable Theories also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Undecidable Theories book for free.

What Is Mathematical Logic

What Is Mathematical Logic Author J. N. Crossley
ISBN-10 9780486151526
Release 2012-08-29
Pages 96
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A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg, Dirac, and others. 1972 edition.

An Outline of Set Theory

An Outline of Set Theory Author James M. Henle
ISBN-10 9780486453378
Release 2007
Pages 145
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An innovative problem-oriented introduction to set theory, this volume is intended for undergraduate courses in which students work in groups on projects and present their solutions to the class. The three-part treatment consists of problems, hints for their solutions, and complete answers. 1986 edition.

Model Theory

Model Theory Author C.C. Chang
ISBN-10 9780486310954
Release 2013-10-03
Pages 672
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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.