Sets, Logic and Categories

ISBN-13: 9781852330569 / Angielski / Miękka / 1999 / 182 str.

Peter J. Cameron

Opis

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, Godel'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."

Recenzje

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.)"

Spis treści

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.