Mathematical Logic

A First Course

By: JOEL W. ROBBIN

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Paperback | 7 July 2006

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238 Pages

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20.9 x 13.6 x 1.91

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Suitable for advanced undergraduates and graduate students, this self-contained text will appeal to readers from diverse fields and varying backgrounds — including mathematics, philosophy, linguistics, computer science, and engineering. It features numerous exercises of varying levels of difficulty, many with solutions.
A survey of the propositional calculus is followed by chapters on first-order logic and first-order recursive arithmetic. An examination of the arithmetization of syntax follows, along with a review of the incompleteness theorems and other applications of the Liar Paradox. The text concludes with a study of second-order logic and an appendix on set theory that will prove valuable to students with little or no mathematical background.

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Preface	p. v
Note to the Student	p. xi
The Propositional Calculus	p. 1
Formation Rules for P	p. 4
Formal Semantics of P	p. 8
Axiomatization of P	p. 14
The Deduction Theorem	p. 16
Some Theorem Schemas of P	p. 20
Completeness	p. 22
First-Order Logic	p. 32
Formation Rules for L([characters not reproducible], X)	p. 34
Free and Bound Variables	p. 37
Models	p. 38
Validity	p. 41
Axiomatization of L([characters not reproducible], X)	p. 43
Propositional Calculus	p. 44
The Deduction Theorem	p. 45
Some Theorems of First-Order Logic	p. 48
The Soundness Theorem	p. 50
The Extension Lemma	p. 52
The Completeness Theorem	p. 54
First-Order Logic with Equality	p. 56
First-Order Recursive Arithmetic	p. 66
Primitive Recursive Functions	p. 66
Some Primitive Recursive Functions	p. 69
Formation Rules for RA	p. 72
Semantics	p. 76
Axiomatics	p. 78
Soundness	p. 80
Sentences without Variables	p. 81
Arithmetization of Syntax	p. 90
Finite Sums and Products	p. 90
Primitive Recursive Relations	p. 91
Definition by Cases and the Least Number Operator	p. 94
Prime Numbers	p. 96
Primitive Recursiveness of the Prime Decomposition	p. 99
Godel Numbers	p. 100
Primitive Recursiveness of the Notion of Function Constant	p. 103
Primitive Recursiveness of the Notion of Term	p. 105
Primitive Recursiveness of the Notion of Wff	p. 106
Substitution	p. 107
Deductions	p. 109
The Incompleteness Theorems and Other Applications of the Liar Paradox	p. 111
The First Godel Incompleteness Theorem	p. 112
Proof of the First Godel Theorem in RA	p. 116
The Second Godel Incompleteness Theorem	p. 117
Tarski's Theorem	p. 119
Arithmetical Sets	p. 121
Recursive Sets and Decision Procedures	p. 122
Church's Theorem for RA	p. 126
Second-Order Logic	p. 132
Formation Rules for L[subscript 2]([characters not reproducible], X)	p. 133
Axiomatics for L[subscript 2]([characters not reproducible], X)	p. 134
Semantics of Second-Order Logic	p. 137
The Completeness Theorem for Second-Order Logic	p. 140
Equality	p. 142
Second-Order Peano Arithmetic	p. 145
Primitive Recursive Functions	p. 148
Numeralwise Representability	p. 153
Godel's Theorem for PA[subscript 2]	p. 156
Church's Theorem for Second-Order Logic	p. 158
Categoricity of PA[subscript 2]	p. 161
Skolem's Paradox	p. 164
Formal Set Theory	p. 166
Appendix	p. 171
Sets and Functions	p. 171
Induction	p. 175
Primitive Recursion	p. 178
Countable Sets	p. 180
Answers to Selected Exercises	p. 183
Suggested Reading	p. 199
Index of Symbols	p. 203
Index	p. 209
Table of Contents provided by Ingram. All Rights Reserved.

Mathematical Logic

A First Course

At a Glance

Paperback

Shipping

How to return your order

Defective items

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