汉密尔顿：数学家的逻辑 Logic for Mathematicians

基本信息

Format:Paperback / softback 240 pages

Publisher:Cambridge University Press

Imprint:Cambridge University Press

Edition:2 Revised edition

ISBN:9780521368650

Published:29 Sep 1988

Weight:368g

Dimensions:232 x 152 x 19 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

这是一本入门教科书，旨在不仅对有意成为逻辑学家的人有用，而且对一般数学家也有用。本书以汉密尔顿博士在斯特灵大学为三年级和四年级本科数学家讲授的课程为基础，旨在向学生或专业数学家介绍数理逻辑的技术和主要结果，这些数学家的背景只需涵盖典型的一年级本科数学课程。在介绍主题时，不偏向特定的方面、应用或发展，试图将其置于数学背景中，并强调逻辑与数学家的相关性。从基础艺术层面开始，文本从非正式讨论进展到形式数学和逻辑系统的准确描述和使用。前几章涵盖了命题和谓词演算。后面的章节讨论了哥德尔关于算术不完备性的定理以及各种不可判定性和不可解性结果，包括对图灵机和抽象可计算性的讨论。每个部分都以练习结束，旨在澄清和巩固该部分的内容。本书末尾提供了许多练习提示或解决方案。这本非常成功的教科书的修订版包括关于 Skolemisation 和将合式公式应用于逻辑编程的新章节。进行了一些更正并添加了额外的练习。

Here is an introductory textbook which is designed to be useful not only to intending logicians but also to mathematicians in general. Based on Dr Hamilton's lectures to third and fourth year undergraduate mathematicians at the University of Stirling it has been written to introduce student or professional mathematicians, whose background need cover no more than a typical first year undergraduate mathematics course, to the techniques and principal results of mathematical logic. In presenting the subject matter without bias towards particular aspects, applications or developments, an attempt has been made to place it in the context of mathematics and to emphasise the relevance of logic to the mathematician. Starting at an elementart level, the text progresses from informal discussion to the precise description and use of formal mathematical and logical systems. The early chapters cover propositional and predicate calculus. The later chapters deal with Gödel's theorem on the incompleteness of arithmetic and with various undecidability and unsolvability results, including a discussion of Turing machines and abstract computability. Each section ends with exercises designed to clarify and consolidate the material in that section. Hints or solutions to many of these are provided at the end of the book. The revision of this very successful textbook includes new sections on Skolemisation and applying well-formed formulas to logic programming. Some corrections have been made and extra exercises added.

作者简介

A.G. Hamilton-Taylor 博士是网络、动画、可视化和电子学习 (WAVE) 研究实验室的创始人，也是牙买加莫纳西印度群岛大学计算机系的讲师。

Dr. A.G. Hamilton-Taylor is founder of the Web, Animation, Visualization and E-learning (WAVE) research lab and lecturer in the Department of Computing, University of the West Indies at Mona, Jamaica.