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TABLE OF CONTENTS

Preface
Introduction
Part I. Propositional Logic
Chapter 1. Language
Chapter 2. Truth Assignments
Chapter 3. Deductions 11
Chapter 4. Soundness and Completeness 15
Hints for Chapters 1{4 17
Part II. First-Order Logic 21
Chapter 5. Languages 23
Chapter 6. Structures and Models 33
Chapter 7. Deductions 41
Chapter 8. Soundness and Completeness 47
Chapter 9. Applications of Compactness 53
Hints for Chapters 5{9 59
Part III. Computability 65
Chapter 10. Turing Machines 67
Chapter 11. Variations and Simulations 75
Chapter 12. Computable and Non-Computable Functions 81
Chapter 13. Recursive Functions 87
Chapter 14. Characterizing Computability 95
Hints for Chapters 10{14 101
Part IV. Incompleteness 109
Chapter 15. Preliminaries 111
Chapter 16. Coding First-Order Logic 113
Chapter 17. De ning Recursive Functions In Arithmetic 117
Chapter 18. The Incompleteness Theorem 123
Hints for Chapters 15{18 127
Appendices 131
Appendix A. A Little Set Theory 133
Appendix B. The Greek Alphabet 135
Appendix C. Logic Limericks 137
Appendix D. GNU Free Documentation License 139
Appendix. Bibliography 147
Appendix. Index 149

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