Axiomatic Set Theory


Author: Patrick Suppes
Publisher: Courier Corporation
ISBN: 0486136876
Category: Mathematics
Page: 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.

Axiomatic Set Theory


Author: Paul Bernays
Publisher: Dover Publications
ISBN: 9780486666372
Category: Mathematics
Page: 256
View: 4616

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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.

A Book of Set Theory


Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486497089
Category: Mathematics
Page: 256
View: 4955

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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"--

Naive Mengenlehre


Author: Paul R. Halmos
Publisher: Vandenhoeck & Ruprecht
ISBN: 9783525405277
Category: Arithmetic
Page: 132
View: 3642

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Set Theory and Logic


Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486139646
Category: Mathematics
Page: 512
View: 2467

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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.

Grundzüge der Mengenlehre


Author: Felix Hausdorff
Publisher: American Mathematical Soc.
ISBN: 9780828400619
Category: Mathematics
Page: 476
View: 4840

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This reprint of the original 1914 edition of this famous work contains many topics that had to be omitted from later editions, notably, Symmetric Sets, Principle of Duality, most of the ``Algebra'' of Sets, Partially Ordered Sets, Arbitrary Sets of Complexes, Normal Types, Initial and Final Ordering, Complexes of Real Numbers, General Topological Spaces, Euclidean Spaces, the Special Methods Applicable in the Euclidean Plane, Jordan's Separation Theorem, the Theory of Content and Measure, the Theory of the Lebesgue Integral. The text is in German.

Introduction to Logic


Author: Patrick Suppes
Publisher: Courier Corporation
ISBN: 0486138054
Category: Mathematics
Page: 336
View: 7713

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Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.

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: 9497

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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

Basic Set Theory


Author: Azriel Levy
Publisher: Courier Corporation
ISBN: 0486150739
Category: Mathematics
Page: 416
View: 9740

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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.

Set Theory and the Continuum Hypothesis


Author: Paul J. Cohen,Martin Davis
Publisher: Courier Corporation
ISBN: 0486469212
Category: Mathematics
Page: 154
View: 8683

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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


Author: James M. Henle
Publisher: Courier Corporation
ISBN: 0486453375
Category: Mathematics
Page: 145
View: 7403

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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.

First Order Mathematical Logic


Author: Angelo Margaris
Publisher: Courier Corporation
ISBN: 9780486662695
Category: Mathematics
Page: 211
View: 3395

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"Attractive and well-written introduction." — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again, and a smooth-running technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to first-order theories, i.e., mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. The book concludes with an outline of Godel's incompleteness theorem. Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises, with selected answers, help students test their grasp of the material. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thought-provoking introduction to the logical underpinnings of mathematical theory. "An excellent text." — Mathematical Reviews

Principia Mathematica.


Author: Alfred North Whitehead,Bertrand Russell
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: 167
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Mathematical Logic

A First Course
Author: Joel W. Robbin
Publisher: Courier Dover Publications
ISBN: 048645018X
Category: Mathematics
Page: 238
View: 2607

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This self-contained text will appeal to readers from diverse fields and varying backgrounds. Topics include 1st-order recursive arithmetic, 1st- and 2nd-order logic, and the arithmetization of syntax. Numerous exercises; some solutions. 1969 edition.

Set Theory

With an Introduction to Real Point Sets
Author: Abhijit Dasgupta
Publisher: Springer Science & Business Media
ISBN: 1461488540
Category: Mathematics
Page: 444
View: 6135

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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.

Foundations and Fundamental Concepts of Mathematics


Author: Howard Eves
Publisher: Courier Corporation
ISBN: 048613220X
Category: Mathematics
Page: 368
View: 7667

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Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.

Introduction to the Foundations of Mathematics

Second Edition
Author: Raymond L. Wilder
Publisher: Courier Corporation
ISBN: 0486276201
Category: Mathematics
Page: 352
View: 3069

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Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.