A Concise Introduction to Mathematical Logic, 3/e (Paperback)

Wolfgang Rautenberg

  • 出版商: Springer
  • 出版日期: 2009-12-17
  • 售價: $3,380
  • 貴賓價: 9.5$3,211
  • 語言: 英文
  • 頁數: 344
  • 裝訂: Paperback
  • ISBN: 1441912207
  • ISBN-13: 9781441912206
  • 相關分類: 邏輯設計 Logic-design
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商品描述

Traditional logic as a part of philosophy is one of the oldest scientific disciplines and can be traced back to the Stoics and to Aristotle. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, and others to create a logistic foundation for mathematics. It steadily developed during the twentieth century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy.

This book treats the most important material in a concise and streamlined fashion. The third edition is a thorough and expanded revision of the former. Although the book is intended for use as a graduate text, the first three chapters can easily be read by undergraduates interested in mathematical logic. These initial chapters cover the material for an introductory course on mathematical logic, combined with applications of formalization techniques to set theory. Chapter 3 is partly of descriptive nature, providing a view towards algorithmic decision problems, automated theorem proving, non-standard models including non-standard analysis, and related topics.

The remaining chapters contain basic material on logic programming for logicians and computer scientists, model theory, recursion theory, Gödel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. Each section of the seven chapters ends with exercises some of which of importance for the text itself. There are hints to most of the exercises in a separate file Solution Hints to the Exercises which is not part of the book but is available from the author’s website.

商品描述(中文翻譯)

傳統邏輯作為哲學的一部分,是最古老的科學學科之一,可以追溯到斯多葛派和亞里士多德。然而,數學邏輯是一門相對年輕的學科,起源於皮亞諾、弗雷格等人為數學創建一個邏輯基礎的努力。它在二十世紀逐漸發展成為一個廣泛的學科,涵蓋多個子領域,並在數學、信息學、語言學和哲學等領域中有眾多應用。

本書以簡潔和簡化的方式介紹了最重要的材料。第三版是對前一版的全面擴充和修訂。雖然本書旨在作為研究生教材使用,但前三章可以很容易地被對數學邏輯感興趣的本科生閱讀。這些初始章節涵蓋了一門關於數學邏輯的入門課程的材料,並結合了形式化技術在集合論中的應用。第三章在一定程度上是描述性的,提供了對算法決策問題、自動定理證明、非標準模型(包括非標準分析)和相關主題的觀點。

其餘章節包含了針對邏輯編程的基礎材料,以及針對邏輯學家和計算機科學家的模型理論、遞歸理論、哥德爾的不完全性定理和數學邏輯的應用。書中討論了數學的哲學和基礎問題。每個章節的最後都有練習題,其中一些對於本文本身非常重要。在一個獨立的文件《解題提示》中提供了大部分練習題的提示,該文件不是本書的一部分,但可以從作者的網站上獲得。