A Book of Set Theory [Pinter] 9780486497082

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. 

頁數：256
版次：第1版
年份：2014年
規格：平裝/單色
ISBN：9780486497082

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 and Related Principles
Chapter 6 The Natural Numbers
Chapter 7 Finite and Infinite Sets
Chapter 8 Arithmetic of Cardinal Numbers
Chapter 9 Arithmetic of the Ordinal Numbers
Chapter 10 Transfinite Recursion. Selected Topics in the Theory of Ordinals and Cardinals
Chapter 11 Consistency and Independence in Set Theory