## Mathematical LogicUndergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part II supplements the material covered in Part I and introduces some of the newer ideas and the more profound results of logical research in the twentieth century. Subsequent chapters introduce the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Gödel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Gödel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. Unabridged republication of the edition published by John Wiley & Sons, Inc. New York, 1967. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index. |

### What people are saying - Write a review

User Review - Flag as inappropriate

I like it!

#### Review: Mathematical Logic

User Review - Ryan O'neil - GoodreadsGreat book, but one piece of advice before you read; find a PDF or intro-to-course online that introduces some of the basic concepts because the author jumps right in pretty quickly. Read full review

### Contents

I | 3 |

II | 8 |

III | 13 |

IV | 17 |

V | 20 |

VI | 22 |

VII | 25 |

VIII | 28 |

XXXIII | 180 |

XXXIV | 183 |

XXXV | 186 |

XXXVI | 191 |

XXXVII | 198 |

XXXVIII | 201 |

XXXIX | 215 |

XL | 223 |

IX | 33 |

X | 39 |

XI | 43 |

XII | 45 |

XIII | 50 |

XIV | 58 |

XV | 67 |

XVI | 74 |

XVII | 83 |

XVIII | 93 |

XIX | 96 |

XX | 101 |

XXI | 107 |

XXII | 112 |

XXIII | 116 |

XXIV | 121 |

XXV | 125 |

XXVI | 134 |

XXVII | 140 |

XXVIII | 148 |

XXIX | 151 |

XXX | 157 |

XXXI | 167 |

XXXII | 175 |

### Common terms and phrases

1(A V B A D B A V B applied argument assignment assume assumption formulas atoms Axiom Schema axiomatic calculus with equality called Church-Turing thesis completeness theorem computation consistency consistency proof contain x free countably inﬁnite counterexample D P(x D-introd decision problem deduction theorem deﬁned deﬁnition domain enumeration equality axioms establish Example Exercise expressions F-part ﬁnd ﬁnite ﬁrst formal system free occurrences free variables function symbols Gentzen given Godel's Hilbert inference integers interpretation intuitionistic ions Kleene Lemma lines logical function mathematics mesons metamathematics method model theory modus ponens natural numbers nonlogical axioms notation number theory number-theoretic object language postulates predicate calculus predicate parameter predicate symbols proof theory propositional calculus provable proved quantiﬁers real numbers recursive replace result rules satisﬁable sequent Similarly simply speciﬁcally substitution true truth table Turing machine V-rule valid consequence Vx3yP(x VxA(x VxP(x VxQ(x