Synopses & Reviews
Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.
Review
"This elementary textbook is an introduction to sets, logic, and categories. The book treats in order naive set theory, ordinal numbers, elementary logic and model theory, axiomatic set theory (through cardinal numbers), and a brief introduction to categories. Exercises are included with some solutions. Remaining solutions are posted on a web site. A brief bibliography is included. The text is clearly written. It would make an excellent first course in foundational issues in mathematics at the undergraduate level. Zentralblatt MATH"
Review
From the reviews:
BULLETIN OF MATHEMATICS BOOKS
"'a well written introduction to logic, with a good dose of set theory (introduction to ordinals and cardinals) and a small dose of categories at the end. (I read this one cover to cover.)"Peter Cameron is a well-known mathematician with an excellent reputation, both as a teacher and as a researcher. The book proposal has had very good reviews and should sell well even though it is a high level text because of Cameron's reputation in the field. The book is a third level text, but this is a relatively popular option for many mathematics students, not least because of the connection between this subject and computational science.
Review
From the reviews: BULLETIN OF MATHEMATICS BOOKS "...a well written introduction to logic, with a good dose of set theory (introduction to ordinals and cardinals) and a small dose of categories at the end. (I read this one cover to cover.)"
Synopsis
Sets, the toolbox for making mathematical models, logic, which tests conclusions, and category theory, the study of functions which preserve some structure on a set together provide the basis for computational science. This self-study guide to all three theories contains many examples.
Table of Contents
Naive Set Theory.- Ordinal Numbers.- Logic.- First-order Logic.- Model theory.- Axiomatic set theory categories.- References.