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Suitable for upper-level undergraduates, this accessible approach to set theory poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity. A historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and sets, functions, relations, partially ordered classes, and the axiom of choice. Other subjects include natural and cardinal numbers, finite and infinite sets, the arithmetic of ordinal numbers, transfinite recursion, and selected topics in the theory of ordinals and cardinals. This updated edition features new material by author Charles C. Pinter.
Chapter 0 Historical Introduction
Chapter 1 Classes and Sets
Chapter 2 Functions
Chapter 3 Relations
Chapter 4 Partially Ordered Classes
Chapter 5 The Axiom of Choice Related Principles
Chapter 6 The Natural Numbers
Chapter 7 Finite and Infinite Sets
Chapter 8 Arthmetic of Cardinal Numbers
Chapter 9 Arthmetic of Ordinal Numbers
Chapter 10 Transfinite Recursion, Selected Topics in the Theory of Ordinals
Chapter 11 Consistency and Independence in Set Theory
지은이: 찰스 핀터(Charles C. Pinter)
Charles Pinter is Professor Emeritus of Mathematics at Bucknell University and the author of Dover's highly successful Book of Abstract Algebra.
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