# Introduction to Mathematical Logic

Princeton University Press, 1996 - Mathematics - 378 pages

Logic 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, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today.

Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic.

Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979 At his death in 1995, Church was still regarded as the greatest mathematical logician in the world.

### What people are saying -Write a review

User Review - Flag as inappropriate

one of the Greatest books on Mathematical Logic.

### Contents

 Logic 1 Names 5 Constants and variables 11 Functions 17 Propositions and propositional functions 27 Improper symbols connectives 33 Operators quantifiers 41 G�dels 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 CHAPTER II The Propositional Calculus Continued 20 The primitive basis of Pg 21 The deduction theorem for P 119 362 120 365 ERRATA 377 Copyright