Introduction to Mathematical Logic

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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.

 

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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
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
CHAPTER II The Propositional Calculus Continued 20 The primitive basis of Pg 21 The deduction theorem for P 119
362
120
365
ERRATA
377
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