| Preface | p. v |
| Note to the Student | p. xi |
| The Propositional Calculus | p. 1 |
| Formation Rules for P | p. 4 |
| Formal Semantics of P | p. 8 |
| Axiomatization of P | p. 14 |
| The Deduction Theorem | p. 16 |
| Some Theorem Schemas of P | p. 20 |
| Completeness | p. 22 |
| First-Order Logic | p. 32 |
| Formation Rules for L([characters not reproducible], X) | p. 34 |
| Free and Bound Variables | p. 37 |
| Models | p. 38 |
| Validity | p. 41 |
| Axiomatization of L([characters not reproducible], X) | p. 43 |
| Propositional Calculus | p. 44 |
| The Deduction Theorem | p. 45 |
| Some Theorems of First-Order Logic | p. 48 |
| The Soundness Theorem | p. 50 |
| The Extension Lemma | p. 52 |
| The Completeness Theorem | p. 54 |
| First-Order Logic with Equality | p. 56 |
| First-Order Recursive Arithmetic | p. 66 |
| Primitive Recursive Functions | p. 66 |
| Some Primitive Recursive Functions | p. 69 |
| Formation Rules for RA | p. 72 |
| Semantics | p. 76 |
| Axiomatics | p. 78 |
| Soundness | p. 80 |
| Sentences without Variables | p. 81 |
| Arithmetization of Syntax | p. 90 |
| Finite Sums and Products | p. 90 |
| Primitive Recursive Relations | p. 91 |
| Definition by Cases and the Least Number Operator | p. 94 |
| Prime Numbers | p. 96 |
| Primitive Recursiveness of the Prime Decomposition | p. 99 |
| Godel Numbers | p. 100 |
| Primitive Recursiveness of the Notion of Function Constant | p. 103 |
| Primitive Recursiveness of the Notion of Term | p. 105 |
| Primitive Recursiveness of the Notion of Wff | p. 106 |
| Substitution | p. 107 |
| Deductions | p. 109 |
| The Incompleteness Theorems and Other Applications of the Liar Paradox | p. 111 |
| The First Godel Incompleteness Theorem | p. 112 |
| Proof of the First Godel Theorem in RA | p. 116 |
| The Second Godel Incompleteness Theorem | p. 117 |
| Tarski's Theorem | p. 119 |
| Arithmetical Sets | p. 121 |
| Recursive Sets and Decision Procedures | p. 122 |
| Church's Theorem for RA | p. 126 |
| Second-Order Logic | p. 132 |
| Formation Rules for L[subscript 2]([characters not reproducible], X) | p. 133 |
| Axiomatics for L[subscript 2]([characters not reproducible], X) | p. 134 |
| Semantics of Second-Order Logic | p. 137 |
| The Completeness Theorem for Second-Order Logic | p. 140 |
| Equality | p. 142 |
| Second-Order Peano Arithmetic | p. 145 |
| Primitive Recursive Functions | p. 148 |
| Numeralwise Representability | p. 153 |
| Godel's Theorem for PA[subscript 2] | p. 156 |
| Church's Theorem for Second-Order Logic | p. 158 |
| Categoricity of PA[subscript 2] | p. 161 |
| Skolem's Paradox | p. 164 |
| Formal Set Theory | p. 166 |
| Appendix | p. 171 |
| Sets and Functions | p. 171 |
| Induction | p. 175 |
| Primitive Recursion | p. 178 |
| Countable Sets | p. 180 |
| Answers to Selected Exercises | p. 183 |
| Suggested Reading | p. 199 |
| Index of Symbols | p. 203 |
| Index | p. 209 |
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