Sets, Logic and Categories

1998
ISBN: 978-1-85233-056-9
Verlag: Springer

Buch, Englisch, 182 Seiten, Paperback, Format (B × H): 178 mm x 235 mm, Gewicht: 345 g

Reihe: Springer Undergraduate Mathematics Series

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Cameron, Peter J.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

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.