## 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

Constants and variables | 9 |

Propositions and propositional functions | 23 |

Operators quantifiers | 39 |

Syntax | 58 |

Definitions | 74 |

Some further theorems and metatheorems of Pi | 91 |

Duality | 106 |

The Propositional Calculus Continued | 119 |

Duality | 201 |

The Pure Functional Calculus of First Order | 218 |

Godels completeness theorem | 233 |

The decision problem solution in special cases | 246 |

Reductions of the decision problem | 270 |

Historical notes | 288 |

Exercises 52 | 302 |

Postulate theory | 317 |

Some further theorems and metatheorems of P2 | 121 |

Other formulations of the propositional calculus | 136 |

Extended propositional calculus and protothetic | 151 |

Functional Calculi of First Order | 168 |

Some theorem schemata of F1 | 186 |

Wellordering of the individuals | 341 |

INDEX OF DEFINITIONS | 357 |

373 | |