| Elementary Mathematical Logic | |
| The propositional calculus | p. 3 |
| Linguistic considerations: formulas | p. 3 |
| Model theory: truth tables, validity | p. 8 |
| Model theory: the substitution rule, a collection of valid formulas | p. 13 |
| Model theory: implication and equivalence | p. 17 |
| Model theory: chains of equivalences | p. 20 |
| Model theory: duality | p. 22 |
| Model theory: valid consequence | p. 25 |
| Model theory: condensed truth tables | p. 28 |
| Proof theory: provability and deducibility | p. 33 |
| Proof theory: the deduction theorem | p. 39 |
| Proof theory: consistency, introduction and elimination rules | p. 43 |
| Proof theory: completeness | p. 45 |
| Proof theory: use of derived rules | p. 50 |
| Applications to ordinary language: analysis of arguments | p. 58 |
| Applications to ordinary language: incompletely stated arguments | p. 67 |
| The predicate calculus | p. 74 |
| Linguistic considerations: formulas, free and bound occurrences of variables | p. 74 |
| Model theory: domains, validity | p. 83 |
| Model theory: basic results on validity | p. 93 |
| Model theory: further results on validity | p. 96 |
| Model theory: valid consequence | p. 101 |
| Proof theory: provability and deducibility | p. 107 |
| Proof theory: the deduction theorem | p. 112 |
| Proof theory: consistency, introduction and elimination rules | p. 116 |
| Proof theory: replacement, chains of equivalences | p. 121 |
| Proof theory: alterations of quantifiers, prenex form | p. 125 |
| Applications to ordinary language: sets, Aristotelian categorical forms | p. 134 |
| Applications to ordinary language: more on translating words into symbols | p. 140 |
| The predicate calculus with equality | p. 148 |
| Functions, terms | p. 148 |
| Equality | p. 151 |
| Equality vs. equivalence, extensionality | p. 157 |
| Descriptions | p. 167 |
| Mathematical Logic and the Foundations of Mathematics | |
| The foundations of mathematics | p. 175 |
| Countable sets | p. 175 |
| Cantor's diagonal method | p. 180 |
| Abstract sets | p. 183 |
| The paradoxes | p. 186 |
| Axiomatic thinking vs. intuitive thinking in mathematics | p. 191 |
| Formal systems, metamathematics | p. 198 |
| Formal number theory | p. 201 |
| Some other formal systems | p. 215 |
| Computability and decidability | p. 223 |
| Decision and computation procedures | p. 223 |
| Turing machines, Church's thesis | p. 232 |
| Church's theorem (via Turing machines) | p. 242 |
| Applications to formal number theory: undecidability (Church) and incompleteness (Godel's theorem) | p. 247 |
| Applications to formal number theory: consistency proofs (Godel's second theorem) | p. 254 |
| Application to the predicate calculus (Church, Turing) | p. 260 |
| Degrees of unsolvability (Post), hierarchies (Kleene, Mostowski) | p. 265 |
| Undecidability and incompleteness using only simple consistency (Rosser) | p. 273 |
| The predicate calculus (additional topics) | p. 283 |
| Godel's completeness theorem: introduction | p. 283 |
| Godel's completeness theorem: the basic discovery | p. 295 |
| Godel's completeness theorem with a Gentzen-type formal system, the Lowenheim-Skolem theorem | p. 305 |
| Godel's completeness theorem (with a Hilbert-type formal system) | p. 312 |
| Godel's completeness theorem, and the Lowenheim-Skolem theorem, in the predicate calculus with equality | p. 315 |
| Skolem's paradox and nonstandard models of arithmetic | p. 321 |
| Gentzen's theorem | p. 331 |
| Permutability, Herbrand's theorem | p. 338 |
| Craig's interpolation theorem | p. 349 |
| Beth's theorem on definability, Robinson's consistency theorem | p. 361 |
| Bibliography | p. 371 |
| Theorem and lemma numbers: pages | p. 386 |
| List of postulates | p. 387 |
| Symbols and notations | p. 388 |
| Index | p. 389 |
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