eBook ISBN:  9781614440284 
Product Code:  CAR/30.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
eBook ISBN:  9781614440284 
Product Code:  CAR/30.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 

Book DetailsThe Carus Mathematical MonographsVolume: 30; 2005; 397 pp
A Tour Through Mathematical Logic provides a tour through the main branches of the foundations of mathematics. It contains chapters covering elementary logic, basic set theory, recursion theory, Gödel's (and others') incompleteness theorems, model theory, independence results in set theory, nonstandard analysis, and constructive mathematics. In addition, this monograph discusses several topics not normally found in books of this type, such as fuzzy logic, nonmonotonic logic, and complexity theory.

Table of Contents

Chapters

Chapter 1. Predicate Logic

Chapter 2. Axiomatic Set Theory

Chapter 3. Recursion Theory and Computability

Chapter 4. Gödel’s Incompleteness Theorems

Chapter 5. Model Theory

Chapter 6. Contemporary Set Theory

Chapter 7. Nonstandard Analysis

Chapter 8. Constructive Mathematics


Reviews

This is a remarkable book, both in terms of the considerable material that it covers and the “user friendliness” with which it is presented ... The way the book is conceived, it seems particularly well suited for small study groups or tutorial sessions in which students first study a particular section on their own, do the exercises, and then seek clarification and help from the instructor. The book would also be welcomed by experienced mathematicians who are interested simply in a quick initiation to some specific topics, such as forcing, nonstandard analysis or constructive mathematics, without having to go through an extensive treatment. All told, the author ought to be commended for having written such a clear and carefully crafted introduction to the whole field of mathematical logic.
Yehuda Rav, Mathematical Reviews


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A Tour Through Mathematical Logic provides a tour through the main branches of the foundations of mathematics. It contains chapters covering elementary logic, basic set theory, recursion theory, Gödel's (and others') incompleteness theorems, model theory, independence results in set theory, nonstandard analysis, and constructive mathematics. In addition, this monograph discusses several topics not normally found in books of this type, such as fuzzy logic, nonmonotonic logic, and complexity theory.

Chapters

Chapter 1. Predicate Logic

Chapter 2. Axiomatic Set Theory

Chapter 3. Recursion Theory and Computability

Chapter 4. Gödel’s Incompleteness Theorems

Chapter 5. Model Theory

Chapter 6. Contemporary Set Theory

Chapter 7. Nonstandard Analysis

Chapter 8. Constructive Mathematics

This is a remarkable book, both in terms of the considerable material that it covers and the “user friendliness” with which it is presented ... The way the book is conceived, it seems particularly well suited for small study groups or tutorial sessions in which students first study a particular section on their own, do the exercises, and then seek clarification and help from the instructor. The book would also be welcomed by experienced mathematicians who are interested simply in a quick initiation to some specific topics, such as forcing, nonstandard analysis or constructive mathematics, without having to go through an extensive treatment. All told, the author ought to be commended for having written such a clear and carefully crafted introduction to the whole field of mathematical logic.
Yehuda Rav, Mathematical Reviews