A Mathematical Introduction to Logic, Second Edition

✍ Scribed by Herbert Enderton, Herbert B. Enderton

• Publisher: Academic Press
• Year: 2001
• Tongue: English
• Leaves: 330
• Edition: 2
• Category: Library

✦ Synopsis

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

Contents......Page 8
Preface......Page 10
Introduction......Page 12
0. Useful Facts about Sets......Page 14
1.0 Informal Remarks on Formal Languages......Page 24
1.1 The Language of Sentential Logic......Page 26
1.2 Truth Assignments......Page 33
1.3 A Parsing Algorithm......Page 42
1.4 Induction and Recursion......Page 47
1.5 Sentential Connectives......Page 58
1.6 Switching Circuits......Page 67
1.7 Compactness and Effectiveness......Page 72
2.0 Preliminary Remarks......Page 80
2.1 First-Order Languages......Page 82
2.2 Truth and Models......Page 93
2.3 A Parsing Algorithm......Page 118
2.4 A Deductive Calculus......Page 122
2.5 Soundness and Completeness Theorems......Page 144
2.6 Models of Theories......Page 160
2.7 Interpretations Between Theories......Page 177
2.8 Nonstandard Analysis......Page 186
3.0 Number Theory......Page 195
3.1 Natural Numbers with Successor......Page 200
3.2 Other Reducts of Number Theory......Page 206
3.3 A Subtheory of Number Theory......Page 215
3.4 Arithmetization of Syntax......Page 237
3.5 Incompleteness and Undecidability......Page 247
3.6 Recursive Functions......Page 260
3.7 Second Incompleteness Theorem......Page 279
3.8 Representing Exponentiation......Page 289
4.1 Second-Order Languages......Page 295
4.2 Skolem Functions......Page 300
4.3 Many-Sorted Logic......Page 308
4.4 General Structures......Page 312
Suggestions For Further Reading......Page 320
List of Symbols......Page 322
Index......Page 324