A Mathematical Introduction to Logic
内容简介
A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.
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作者简介
Herbert B.Enderton，哈佛大学博士，师从著名哲学家hilary putnam。曾任教于加州大学伯克利分校。现为加州大学洛杉矶分校数学系兼职教授，该校“逻辑学论坛”主席，曾担任《符号逻辑学会评论》杂志的主编。除本书外，他还著有另外两本广受好评的教材elements of set theory（影印版已经由人民邮电出版社出版）和linear algebra。
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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
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读书文摘
We call these objects "symbols," but we remain neutral as to what the exact ontological status of symbols might be.
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