A MATHEMATICAL INTRODUCTION TO LOGICPDF电子书下载

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INTRODUCTION 1

Chapter Zero—USEFUL FACTS ABOUT SETS 4

Chapter One—SENTENTIAL LOGIC 14

1.0 Informal Remarks on Formal Languages 14

1.1 The Language of Sentential Logic 17

1.2 Induction and Recursion 22

1.3 Truth Assignments 30

1.4 Unique Readability 39

1.5 Sentential Connectives 44

1.6 Switching Circuits 53

1.7 Compactness and Effectiveness 58

Chapter Two—FIRST-ORDER LOGIC 65

2.0 Preliminary Remarks 65

2.1 First-Order Languages 67

2.2 Truth and Models 79

2.3 Unique Readability 97

2.4 A Deductive Calculus 101

2.5 Soundness and Completeness Theorems 124

2.6 Models of Theories 140

2.7 Interpretations between Theories 154

2.8 Nonstandard Analysis 164

Chapter Three—UNDECIDABILITY 174

3.0 Number Theory 174

3.1 Natural Numbers with Successor 178

3.2 Other Reducts of Number Theory 184

3.3 A Subtheory of Number Theory 193

3.4 Arithmetization of Syntax 217

3.5 Incompleteness and Undecidability 227

3.6 Applications to Set Theory 239

3.7 Representing Exponentiation 245

3.8 Recursive Functions 251

Chapter Four—SECOND-ORDER LOGIC 268

4.1 Second-Order Languages 268

4.2 Skolem Functions 274

4.3 Many-Sorted Logic 277

4.4 General Structures 281

Index 291

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