A mathematical introduction to logic = 数理逻辑 / 2nd ed.
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ISBN：9787115141453
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简介
本书是数理逻辑方面的经典教材。书中涵盖了命题逻辑、一阶逻辑、不可判定性以及二阶逻辑等方面的内容，并且包含了与计算机科学有关的主题，如有限模型。本书特点是：内容可读性强；组织结构更灵活，授课教师可根据教学需要节选本书的内容；反映了近几年来理论计算机科学对逻辑学产生的影响；包含较多的示例和说明。本书适合作为计算机及相关专业本科生和研究生数理逻辑课程的教材。.
本书是数理逻辑方面的经典教材，以可读性强而著称，在美国大学中采用率极高，麻省理工学院、加州大学伯克利分校、哥伦比亚大学、康奈尔大学等众多名校均用它作为教材。本版章节组织更加灵活，增加了与计算机科学相关的主题(比如有限模型)，还增加了一些示例和阐释文字，更适合本科生和研究生数理逻辑课程使用。.
本书内容严密、完整、一致，很好地介绍了逻辑实践……
——douglas cannon,华盛顿大学.
这本书写作思路清晰缜密，我采用这本书作为教材的原因是，它详细且严密地讲解了谓词演算，详细且极好地讨论了不完备性现象，并且采用伯克利学派开发的标准记号。
——karel prikry，明尼苏达大学..
本书数学上非常严格，而且示例比其他图书都丰富。因此我已经决定将本书用作教材。
——sun-joo shin，圣母大学...
目录
CHAPTER ZERO Useful Facts about Sets 1
CHAPTER ONE Sentential Logic 11
1.0 Informal Remarks on Formal Languages 11
1.1 The Language of Sentential Logic 13
1.2 Truth Assignments 20
1.3 A Parsing Algorithm 29
1.4 Induction and Recursion 34
1.5 Sentential Connectives 45
1.6 Switching Circuits 54
1.7 Compactness and Effectiveness 59
CHAPTER TWO First-Order Logic 67
2.0 Preliminary Remarks 67
2. l First-Order Languages 69
2.2 Truth and Models 80
2.3 A Parsing Algorithm 105
2.4 A Deductive Calculus 109
2.5 Soundness and Completeness Theorems 131
2.6 Models of Theories 147
2.7 Interpretations Between Theories 164
2.8 Nonstandard Analysis 173
CHAPTER THREE Undecidability 182
3.0 Number Theory 182
3.1 Natural Numbers with Successor 187
3.2 Other Reducts of Number Theory 193
3.3 A Subtheory of Number Theory 202
3.4 Arithmetization of Syntax 224
3.5 Incompleteness and Undecidability 234
3.6 Recursive Functions 247
3.7 Second Incompleteness Theorem 266
3.8 Representing Exponentiation 276
CHAPTER FOUR Second-Order Logic 282
4.1 Second-Order Languages 282
4.2 Skolem Functions 287
4.3 Many-Sorted Logic 295
4.4 General Structures 299
SUGGESTIONS FOR FURTHER READING 307
LIST OF SYMBOLS 309
INDEX
CHAPTER ONE Sentential Logic 11
1.0 Informal Remarks on Formal Languages 11
1.1 The Language of Sentential Logic 13
1.2 Truth Assignments 20
1.3 A Parsing Algorithm 29
1.4 Induction and Recursion 34
1.5 Sentential Connectives 45
1.6 Switching Circuits 54
1.7 Compactness and Effectiveness 59
CHAPTER TWO First-Order Logic 67
2.0 Preliminary Remarks 67
2. l First-Order Languages 69
2.2 Truth and Models 80
2.3 A Parsing Algorithm 105
2.4 A Deductive Calculus 109
2.5 Soundness and Completeness Theorems 131
2.6 Models of Theories 147
2.7 Interpretations Between Theories 164
2.8 Nonstandard Analysis 173
CHAPTER THREE Undecidability 182
3.0 Number Theory 182
3.1 Natural Numbers with Successor 187
3.2 Other Reducts of Number Theory 193
3.3 A Subtheory of Number Theory 202
3.4 Arithmetization of Syntax 224
3.5 Incompleteness and Undecidability 234
3.6 Recursive Functions 247
3.7 Second Incompleteness Theorem 266
3.8 Representing Exponentiation 276
CHAPTER FOUR Second-Order Logic 282
4.1 Second-Order Languages 282
4.2 Skolem Functions 287
4.3 Many-Sorted Logic 295
4.4 General Structures 299
SUGGESTIONS FOR FURTHER READING 307
LIST OF SYMBOLS 309
INDEX
A mathematical introduction to logic = 数理逻辑 / 2nd ed.
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