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.

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. Includes supplementary material: sn.pub/extras

Klappentext

Naive Set Theory.- Ordinal Numbers.- Logic.- First-order Logic.- Model theory.- Axiomatic set theory categories.- References.

Zusammenfassung

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.)"

Inhalt

1. Naïve set theory.- 2. Ordinal numbers.- 3. Logic.- 4. First-order logic.- 5. Model theory.- 6. Axiomatic set theory.- 7. Categories.- 8. Where to from here?.- Solutions to selected exercises.- References.