Introduction to Mathematical Logic

Front Cover
Princeton University Press, 1996 - Mathematics - 378 pages
1 Review

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

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
INDEX OF AUTHORS CITED
373
Copyright

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information