I know we have a few set theorists here, so:

Can anybody recommend a good book on set theory? I do not require a “beginners book”, i.e. one that starts from scratch explaining subsets etc. and takes an age to get going, rather I’d like a book detailing stuff like the axiom of choice, ordinals and transfinite stuff, Cantor’s proofs etc.

I’m currently reading Stoll’s “Set Theory and Logic”, but I’m not particularly impressed (there’s far too much text and not enough theorems).

If any texts also include explanation/introduction (perhaps in some appendix or advanced chapter) to Fraenkel-Mostowski set theory, or ZFA, then this will be a bonus.

Many thanks.

One of the standard texts is Kenneth Kunen’s Set Theory: An Introduction to Independence Proofs. It covers a lot of material, but it’s a fairly advanced book and is difficult to read.

More accessible (but not as thorough) are *Discovering Modern Set Theory, Vols* I and II, by Just and Weese.

A few books that might be worth looking at:

[ul]

[li]Patrick Suppes’s “Axiomatic Set Theory”. This seems to be a pretty readable and concise introduction for someone who has an informal background.[/li][li]Elliott Mendelson’s “Introduction to Mathematical Logic”. Despite its friendly-sounding title, this is a pretty serious math book. There’s a chapter on set theory that might be worth looking at.[/li][li]W. V. Quine’s “Set Theory and Its Logic”. I can’t vouch for this one personally, but it’s a classic.[/li][/ul]

If nothing else, browsing around the related items for these on your local Amazon site might give you some ideas.

On preview, I see **Cabbage** has weighed in. I’d look at his recs first, but these might be interesting anyway.

These look like they contain a lot of what I’m after. Thanks for the suggestions, both.