《A MATHEMATICAL INTRODUCTION TO LOGIC》求取 ⇩

INTRODUCTION1

Chapter Zero—USEFUL FACTS ABOUT SETS4

Chapter One—SENTENTIAL LOGIC14

1.0 Informal Remarks on Formal Languages14

1.1 The Language of Sentential Logic17

1.2 Induction and Recursion22

1.3 Truth Assignments30

1.4 Unique Readability39

1.5 Sentential Connectives44

1.6 Switching Circuits53

1.7 Compactness and Effectiveness58

Chapter Two—FIRST-ORDER LOGIC65

2.0 Preliminary Remarks65

2.1 First-Order Languages67

2.2 Truth and Models79

2.3 Unique Readability97

2.4 A Deductive Calculus101

2.5 Soundness and Completeness Theorems124

2.6 Models of Theories140

2.7 Interpretations between Theories154

2.8 Nonstandard Analysis164

Chapter Three—UNDECIDABILITY174

3.0 Number Theory174

3.1 Natural Numbers with Successor178

3.2 Other Reducts of Number Theory184

3.3 A Subtheory of Number Theory193

3.4 Arithmetization of Syntax217

3.5 Incompleteness and Undecidability227

3.6 Applications to Set Theory239

3.7 Representing Exponentiation245

3.8 Recursive Functions251

Chapter Four—SECOND-ORDER LOGIC268

4.1 Second-Order Languages268

4.2 Skolem Functions274

4.3 Many-Sorted Logic277

4.4 General Structures281

Index291