Logic, Induction and Sets (London Mathematical Society Student Texts) Review

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Logic, Induction and Sets (London Mathematical Society Student Texts) ReviewAs a regular reviewer who reads the books he reviews, I am beginning to find a routine sameness to many of the books I examine. This holds for introductory logic, some areas of which have not changed for thousands of years. In many cases, it has become so routine that it is very hard to read the books, and to solve this problem I have adopted the solution that I read approximately ten pages at a time. Most books covering this material are a sequential listing and proving of the fundamental theorems. Correct, but hardly a point of differentiation between books.
Fortunately, I found this book to be different. The author uses more explanatory text and fewer equations than most others do. While that alone does not make it better, the quality of the exposition does. There was more enthusiasm generated when reading this book than I have had in a long time when reading an introductory mathematics book. There was no reason to adopt the ten page rule. Despite the relative lack of equations, all of the basics are covered in sufficient detail. One hundred and thirty eight exercises are interspersed within the text and solutions to approximately one fourth of the exercises are included.
A book that can be used as a textbook or for self-study, it manages to be different enough to read easily, but not so different that it is difficult to learn from.Logic, Induction and Sets (London Mathematical Society Student Texts) OverviewPhilosophical considerations, which are often ignored or treated casually, are given careful consideration in this introduction. Thomas Forster places the notion of inductively defined sets (recursive datatypes) at the center of his exposition resulting in an original analysis of well established topics.The presentation illustrates difficult points and includes many exercises. Little previous knowledge of logic is required and only a knowledge of standard undergraduate mathematics is assumed.

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