Introduction to mathematical logic
著者
書誌事項
Introduction to mathematical logic
Chapman & Hall/CRC, 2001
4th ed
並立書誌 全1件
大学図書館所蔵 全4件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references(p. [412]-423) and index
Reprint. Originally published by Chapman & Hall, c1997
内容説明・目次
内容説明
The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them.
Introduction to Mathematical Logic includes:
propositional logic
first-order logic
first-order number theory and the incompleteness and undecidability theorems of Goedel, Rosser, Church, and Tarski
axiomatic set theory
theory of computability
The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.
目次
The Propositional Calculus
Propositional Connectives. Truth Tables
Tautologies
Adequate Sets of Connectives
An Axiom System for the Propositional Calculus
Independence: Many-Valued Logics
Other Axiomatizations
Quantification Theory
Quantifiers
First-Order Languages and Their Interpretations
First-Order Theories
Properties of First-Order Theories
Additional Metatheorems and Derived Rules
Rule C
Completeness Theorems
First-Order Theories with Equality
Definitions of New Function Letters and Individual Constants
Prenex Normal Forms
Isomorphism of Interpretations. Categoricity of Theories
Generalized First-Order Theories. Completeness and Decidability
Elementary Equivalence. Elementary Extensions
Ultrapowers. Non-Standard Analysis
Semantic Trees
Quantification Theory Allowing Empty Domains
Formal Number Theory
An Axiom System
Number-Theoretic Functions and Relations
Primitive Recursive and Recursive Functions
Arithmatization. Goedel Numbers
The Fixed Point Theorem. Goedel's Incompleteness Theorem
Recursive Undecidability. Church's Theorem
Axiomatic Set Theory
An Axiom System
Ordinal Numbers
Equinumerousity. Finite and Denumerable Sets.
Hartog's Theorem. Initial Ordinals. Ordinal Arithmetic
The Axiom of Choice. The Axiom of Regularity
Other Axiomatizations of Set Theory
Computability
Algorithms. Turing Machines
Diagrams
Partial Recursive Functions. Unsolvable Problems.
The Kleene-Mosotovski Hierarchy. Recursively Enumerable Sets
Other notions of Computability
Decision Problems
「Nielsen BookData」 より