9780122384523

A Mathematical Introduction to Logic

by ;
  • ISBN13:

    9780122384523

  • ISBN10:

    0122384520

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 12/22/2000
  • Publisher: Elsevier Science

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Supplemental Materials

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Summary

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets. * Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. * Reduced mathematical rigour to fit the needs of undergraduate students

Table of Contents

Preface ix
Introduction xi
Useful Facts about Sets
1(10)
Sentential Logic
11(56)
Informal Remarks on Formal Languages
11(2)
The Language of Sentential Logic
13(7)
Truth Assignments
20(9)
A Parsing Algorithm
29(5)
Induction and Recursion
34(11)
Sentential Connectives
45(9)
Switching Circuits
54(5)
Compactness and Effectiveness
59(8)
First-Order Logic
67(115)
Preliminary Remarks
67(2)
First-Order Languages
69(11)
Truth and Models
80(25)
A Parsing Algorithm
105(4)
A Deductive Calculus
109(22)
Soundness and Completeness Theorems
131(16)
Models of Theories
147(17)
Interpretations Between Theories
164(9)
Nonstandard Analysis
173(9)
Undecidability
182(100)
Number Theory
182(5)
Natural Numbers with Successor
187(6)
Other Reducts of Number Theory
193(9)
A Subtheory of Number Theory
202(22)
Arithmetization of Syntax
224(10)
Incompleteness and Undecidability
234(13)
Recursive Functions
247(19)
Second Incompleteness Theorem
266(10)
Representing Exponentiation
276(6)
Second-Order Logic
282(25)
Second-Order Languages
282(5)
Skolem Functions
287(8)
Many-Sorted Logic
295(4)
General Structures
299(8)
Suggestions for Further Reading 307(2)
List of Symbols 309(2)
Index 311

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