Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic Volume II: Foundations of Mathematics

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This book provides an introduction to mathematical logic and the foundations of mathematics. It will help prepare students for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The presentation of finite state and Turing machines leads to the Halting Problem and Gödel's Incompleteness Theorem, which have broad academic interest, particularly in computer science and philosophy. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Introduction Contents: Preface About the Authors Introduction Propositional Logic Predicate Logic Models of Predicate Logic Boolean Algebras Computability Decidable and Undecidable Theories Algorithmic Randomness Nonstandard Numbers Foundations of Geometry Bibliography Index Readership: Advanced undergraduate or beginning graduate students interested in mathematical logic, mathematics, computer science, and philosophy.

A BOOK OF SET THEORY (1版)

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A Book of Set Theory +作者：Pinter +年份：2014 年1 版 +ISBN：9780486497082 +書號：MA0378P +規格：平裝/單色 +頁數：256 +出版商：Dover 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. 目錄 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