点击选择搜索分类
首页 - 社会科学- 正文
☆☆☆☆☆
||
[德] 艾宾浩斯 著
出版社: 世界图书出版公司 ISBN:9787506292276 版次:1 商品编码:10096474 包装:平装 外文名称:Mathematical Logic 开本:24开 出版时间:2008-05-01 用纸:胶版纸 页数:289 正文语种:英语
Godels incompleteness theorems are presented in connection with several related results (such as Trahtenbrots theorem) which all exemplify the limitatious of machine-oriented proof methods. The notions of computability theory that are relevant to this discussion are given in detail. The concept of computability is made precise by means of the register machine as a
Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godels completeness theorem, which shows that the consequence relation coincides with formal provability: By means of a calculus consisting of simple formal inference rules, one can obtain all consequences of a given axiom system (and in particular, imitate all mathematical proofs)
PART A
ⅠIntroduction
1.An Example from Group Theory
2.An Example from the Theory of Equivalence Relations
3.A Preliminary Analysis
4.Preview
Ⅱ Syntax of First-Order Languages
1.Alphabets
2.The Alphabet of a First-Order Language
3.Terms and Formulas in First-Order Languages
4.Induction in the Calculus of Terms and in the Calculus of Formulas
5.Free Variables and Sentences
Ⅲ Semantics of First-Order Languages
1.Structures and Interpretations
2.Standardization of Connectives
3.The Satisfaction Relation
4.The Consequence Relation
5.Two Lemmas on the Satisfaction Relation
6.Some simple formalizations
7.Some remarks on Formalizability
8.Substitution
Ⅳ A Sequent Calculus
1.Sequent Rules
2.Structural Rules and Connective Rules
3.Derivable Connective Rules
4.Quantifier and Equality Rules
5.Further Derivable Rules and Sequents
6.Summary and Example
7.Consistency
ⅤThe Completeness Theorem
1.Henkin’S Theorem.
2. Satisfiability of Consistent Sets of Formulas(the Countable Casel
3. Satisfiability of Consistent Sets of Formulas(the General Case)
4.The Completeness Theorem
Ⅵ The LSwenheim-Skolem and the Compactness Theorem
1.The L6wenheim-Skolem Theorem.
2.The Compactness Theorem
3.Elementary Classes
4.Elementarily Equivalent Structures
Ⅶ The Scope of First-Order Logic
1.The Notion of Formal Proof
2.Mathematics Within the Framework of Fimt—Order Logic
3.The Zermelo-Fraenkel Axioms for Set Theory.
4.Set Theory as a Basis for Mathematics
Ⅷ Syntactic Interpretations and Normal Forms
1.Term-Reduced Formulas and Relational Symbol Sets
2.Syntactic Interpretations
3.Extensions by Definitions
4.Normal Forms
PART B
Ⅸ Extensions of First-order logic
Ⅹ Limitations of the Formal Method
Ⅺ Free Models and Logic Programming
Ⅻ An Algebraic Characterization of Elementary Equivalence
ⅩⅢ Lindstrom’s Theorems
References
Symbol Index
Subject Index
数理逻辑(第2版) [Mathematical Logic] 电子书 下载 mobi epub pdf txt
数理逻辑(第2版) [Mathematical Logic]-so88
数理逻辑(第2版) [Mathematical Logic] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[德] 艾宾浩斯 著
出版社: 世界图书出版公司 ISBN:9787506292276 版次:1 商品编码:10096474 包装:平装 外文名称:Mathematical Logic 开本:24开 出版时间:2008-05-01 用纸:胶版纸 页数:289 正文语种:英语
编辑推荐
A short digression into model theory will help us to analyze the expressive power of the first-order language, and it will turn out that there are certain deficiencies. For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand, this di~culty can be overcome——-even in the framework of first-order logic——by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.Godels incompleteness theorems are presented in connection with several related results (such as Trahtenbrots theorem) which all exemplify the limitatious of machine-oriented proof methods. The notions of computability theory that are relevant to this discussion are given in detail. The concept of computability is made precise by means of the register machine as a
内容简介
What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs?Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godels completeness theorem, which shows that the consequence relation coincides with formal provability: By means of a calculus consisting of simple formal inference rules, one can obtain all consequences of a given axiom system (and in particular, imitate all mathematical proofs)
内页插图
目录
PrefacePART A
ⅠIntroduction
1.An Example from Group Theory
2.An Example from the Theory of Equivalence Relations
3.A Preliminary Analysis
4.Preview
Ⅱ Syntax of First-Order Languages
1.Alphabets
2.The Alphabet of a First-Order Language
3.Terms and Formulas in First-Order Languages
4.Induction in the Calculus of Terms and in the Calculus of Formulas
5.Free Variables and Sentences
Ⅲ Semantics of First-Order Languages
1.Structures and Interpretations
2.Standardization of Connectives
3.The Satisfaction Relation
4.The Consequence Relation
5.Two Lemmas on the Satisfaction Relation
6.Some simple formalizations
7.Some remarks on Formalizability
8.Substitution
Ⅳ A Sequent Calculus
1.Sequent Rules
2.Structural Rules and Connective Rules
3.Derivable Connective Rules
4.Quantifier and Equality Rules
5.Further Derivable Rules and Sequents
6.Summary and Example
7.Consistency
ⅤThe Completeness Theorem
1.Henkin’S Theorem.
2. Satisfiability of Consistent Sets of Formulas(the Countable Casel
3. Satisfiability of Consistent Sets of Formulas(the General Case)
4.The Completeness Theorem
Ⅵ The LSwenheim-Skolem and the Compactness Theorem
1.The L6wenheim-Skolem Theorem.
2.The Compactness Theorem
3.Elementary Classes
4.Elementarily Equivalent Structures
Ⅶ The Scope of First-Order Logic
1.The Notion of Formal Proof
2.Mathematics Within the Framework of Fimt—Order Logic
3.The Zermelo-Fraenkel Axioms for Set Theory.
4.Set Theory as a Basis for Mathematics
Ⅷ Syntactic Interpretations and Normal Forms
1.Term-Reduced Formulas and Relational Symbol Sets
2.Syntactic Interpretations
3.Extensions by Definitions
4.Normal Forms
PART B
Ⅸ Extensions of First-order logic
Ⅹ Limitations of the Formal Method
Ⅺ Free Models and Logic Programming
Ⅻ An Algebraic Characterization of Elementary Equivalence
ⅩⅢ Lindstrom’s Theorems
References
Symbol Index
Subject Index
前言/序言
数理逻辑(第2版) [Mathematical Logic] 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 探秘海洋生物(全彩版)/科学眼 (日) 原田雅章著
- 华夏万卷·历代传世碑帖精粹彩色本24:赵孟頫行书洛神赋
- 科学外史
- 中国书法研究系列:晋唐草书笔法探源
- 开心农场-第八辑科学读本A本
- 禽病理及诊治精要/普通高等教育“十二五”畜牧兽医类规划教材
- 奥雅绘画小课堂-3-随书附赠奥雅密语卡
- 肉鸭健康养殖百问百答
- 图说科学百科 9787511223777
- 西泠印社精选历代碑帖:吴熙载篆书崔子玉座右铭
- 正版 动物手绘图谱 哺乳动物 9787545217254 曾日明 上海世纪出版股份有限公司
- 普通高等教育“十二五”规划教材·全国高职高专园林类专业规划教材:花卉装饰技术
- 世界科普巨匠经典译丛:走向光明 [苏] 米·伊林,丁荣立
- 草本花卉工培训教材
- 贪婪的狐狸-做最棒的自己双语绘本-汉英对照