Peter J. Cameron

Sets, Logic and Categories

This book is published by Springer-Verlag, in the Springer Undergraduate Mathematics Series, in February 1999.

Another book in the series is Geoff Smith's Introductory Mathematics: Algebra and Analysis.

A PDF file of the preface and table of contents is available.

Solutions to the exercises (PDF files):

• Chapter 1: Naive set theory
• Chapter 2: Ordinal numbers
• Chapter 3: Logic
• Chapter 4: First-order logic

Here is a list of known misprints, together with comments and improvements from various readers.

From the review by A. M. Coyne in Zentralblatt für Mathematik:

The text is clearly written. It would make an excellent first course in foundational issues in mathematics at the undergraduate level.

Further references

• For topos theory: S. MacLane & I. Moerdijk, Sheaves in Geometry and Logic: A first introduction to topos theory, Springer 1990. (Suggested by Steve Awodey.)
• A computer scientist's view: Paul Taylor, Practical Foundations of Mathematics, Cambridge University Press, 1999.
• A book about how our brains are wired to do mathematics: Brian Butterworth, The Mathematical Brain, Macmillan, London, 1999.
• "Journey into a Dark Heart", by Peter Høeg, from Tales of the Night, Harville Press, London, 1990, features Gödel's Theorem as part of the plot.

Interesting links

• Venn diagrams by Frank Ruskey
• Beginnings of set theory (on MacTutor History of Mathematics site at St Andrews)
• British Logic Colloquium (with many further links!)
• Theory and Applications of Categories (electronic journal)
• Gödel on the Net
• Fast-growing functions and unprovable theorems by Andrew Burbanks
• Joshu's Mu: further information by Richard Leedham-Green

Peter J. Cameron
27 January 2003.