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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"--

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.

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.

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.

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.

Introduction to the Theory of Sets

Introduction to the Theory of Sets Author Joseph Breuer
ISBN-10 9780486154879
Release 2012-08-09
Pages 128
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This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.

Naive Set Theory

Naive Set Theory Author Paul R. Halmos
ISBN-10 9780486814872
Release 2017-04-19
Pages 112
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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.

Theory of Sets

Theory of Sets Author E. Kamke
ISBN-10 9780486450834
Release 2006
Pages 144
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This introduction to the theory of sets employs the discoveries of Cantor, Russell, Weierstrass, Zermelo, Bernstein, Dedekind, and others. It analyzes concepts and principles, offering numerous examples. Topics include the rudiments of set theory, arbitrary sets and their cardinal numbers, ordered sets and their order types, and well-ordered sets and their ordinal numbers. 1950 edition.

Set Theory and Logic

Set Theory and Logic Author Robert R. Stoll
ISBN-10 9780486139647
Release 2012-05-23
Pages 512
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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.

Axiomatic Set Theory

Axiomatic Set Theory Author Paul Bernays
ISBN-10 0486666379
Release 1991-02-01
Pages 256
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A monograph containing a historical introduction by A. A. Fraenkel to the original Zermelo-Fraenkel form of set-theoretic axiomatics, and Paul Bernays’ independent presentation of a formal system of axiomatic set theory. No special knowledge of set thory and its axiomatics is required. With indexes of authors, symbols and matters, a list of axioms and an extensive bibliography.

Classic Set Theory

Classic Set Theory Author D.C. Goldrei
ISBN-10 9781351460606
Release 2017-09-06
Pages 296
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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.

Philosophical Introduction to Set Theory

Philosophical Introduction to Set Theory Author Stephen Pollard
ISBN-10 9780486805825
Release 2015-07-20
Pages 192
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The primary mechanism for ideological and theoretical unification in modern mathematics, set theory forms an essential element of any comprehensive treatment of the philosophy of mathematics. This unique approach to set theory offers a technically informed discussion that covers a variety of philosophical issues. Rather than focusing on intuitionist and constructive alternatives to the Cantorian/Zermelian tradition, the author examines the two most important aspects of the current philosophy of mathematics, mathematical structuralism and mathematical applications of plural reference and plural quantification. Clearly written and frequently cited in the mathematical literature, this book is geared toward advanced undergraduates and graduate students of mathematics with some aptitude for mathematical reasoning and prior exposure to symbolic logic. Suitable as a source of supplementary readings in a course on set theory, it also functions as a primary text in a course on the philosophy of mathematics.

Introduction to Axiomatic Set Theory

Introduction to Axiomatic Set Theory Author G. Takeuti
ISBN-10 9781468499155
Release 2013-12-01
Pages 251
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In 1963, the first author introduced a course in set theory at the Uni versity of Illinois whose main objectives were to cover G6del's work on the consistency of the axiom of choice (AC) and the generalized con tinuum hypothesis (GCH), and Cohen's work on the independence of AC and the GCH. Notes taken in 1963 by the second author were the taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are highlighted, and second, the student who wishes to master the sub ject is compelled to develop the details on his own. However, an in structor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text. We have chosen instead a development that is quite detailed and complete. For our slow development we claim the following advantages. The text is one from which a student can learn with little supervision and instruction. This enables the instructor to use class time for the presentation of alternative developments and supplementary material.

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.

Probability Theory

Probability Theory Author Alfred Renyi
ISBN-10 9780486458670
Release 2007-05-11
Pages 666
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The founder of Hungary's Probability Theory School, A. Rényi made significant contributions to virtually every area of mathematics. This introductory text is the product of his extensive teaching experience and is geared toward readers who wish to learn the basics of probability theory, as well as those who wish to attain a thorough knowledge in the field. Based on the author's lectures at the University of Budapest, this text requires no preliminary knowledge of probability theory. Readers should, however, be familiar with other branches of mathematics, including a thorough understanding of the elements of the differential and integral calculus and the theory of real and complex functions. These well-chosen problems and exercises illustrate the algebras of events, discrete random variables, characteristic functions, and limit theorems. The text concludes with an extensive appendix that introduces information theory.

Group Theory

Group Theory Author W. R. Scott
ISBN-10 9780486140162
Release 2012-05-23
Pages 512
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Here is clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.

The Philosophy of Set Theory

The Philosophy of Set Theory Author Mary Tiles
ISBN-10 0486435202
Release 2004
Pages 239
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A century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled him to derive theorems that established a mathematical reality for a hierarchy of infinities. Cantor's innovation was opposed, and ignored, by the establishment; years later, the value of his work was recognized and appreciated as a landmark in mathematical thought, forming the beginning of set theory and the foundation for most of contemporary mathematics. As Cantor's sometime collaborator, David Hilbert, remarked, "No one will drive us from the paradise that Cantor has created." This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory; logical objects and logical types; and independence results and the universe of sets. She concludes with views of the constructs and reality of mathematical structure. Philosophers with only a basic grounding in mathematics, as well as mathematicians who have taken only an introductory course in philosophy, will find an abundance of intriguing topics in this text, which is appropriate for undergraduate-and graduate-level courses.