## Introduction to Mathematical LogicLogic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, Even beyond the accomplishment of that book, however, his second Princeton book, Church was one of the principal founders of the Association for Symbolic Logic; he founded the |

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### Contents

Logic | 1 |

Names | 5 |

Constants and variables | 11 |

Functions | 17 |

Propositions and propositional functions | 27 |

Improper symbols connectives | 33 |

Operators quantifiers | 41 |

Gödels completeness theorem | 44 |

Formulations employing axiom schemata | 148 |

Historical notes | 159 |

69 | 163 |

86 | 166 |

93 | 167 |

Functional Calculi of First Order | 168 |

Propositional calculus | 179 |

Consistency of | 185 |

The logistic method | 49 |

Syntax | 59 |

Semantics 1 1 | 65 |

3 | 67 |

9 | 68 |

The Propositional Calculus 10 The primitive basis of | 69 |

Definitions | 79 |

Theorems of Pa Exercises 12 | 85 |

The deduction theorem | 87 |

Some further theorems and metatheorems of | 91 |

Exercises 14 | 93 |

Tautologies the decision problem | 95 |

Exercises 15 | 102 |

Duality | 107 |

Consistency | 108 |

Completeness | 111 |

Exercises 18 | 112 |

Independence | 113 |

Some further theorems and metatheorems of | 121 |

Primitive connectives for the propositional calculus | 131 |

Exercises 19 | 134 |

Partial systems of propositional calculus | 140 |

Derived rules of substitution | 193 |

Duality | 203 |

Prenex normal form | 211 |

The Pure Functional Calculus of First Order | 218 |

Skolem normal form | 225 |

102 | 246 |

109 | 255 |

Reductions of the decision problem | 271 |

Functional calculus of first order with equality | 281 |

Historical notes | 289 |

111 | 294 |

Functional Calculi of Second Order | 295 |

Equality | 301 |

Henkins completeness theorem | 315 |

112 | 337 |

115 | 339 |

Wellordering of the individuals | 341 |

Exercises 58 | 354 |

362 | |

365 | |

ERRATA | 377 |

### Other editions - View all

Introduction to Mathematical Logic, Volume 1 Alonzo Church,Clifford Truesdell No preview available - 1956 |