Sets, Logic and Categories

by Peter J. Cameron

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.

Genres: Mathematics, Logic

Paperback

First published January 22, 1999

Reviews

[Robert · Rating 4 out of 5]

Category theory was all the rage amongst a certain group of people when I was in graduate school (I was friends with some programming language students).

I wanted to get in on the fun hence getting this.

I didn't get as much out of it as I'd wished, but I also haven't seen any other book that is clearer.

At this point I am not sure if I will ever want to seriously study category theory, but if I did this would definitely be my starting point.

I really like the style and in fact the entire "Springer Undergraduate Mathematics Series".

It's about as gentle as you could find with all the things you could typically want, plenty of examples, explanations and exercises with a clear emphasis on key concepts and lots of motivation.

Now this came out a while ago so perhaps there is something newer and better, but on the other hand the basics haven't changed, so it should still be good!