Can you suggest a good book for set theory?
I have just started reading about Group theory and want to learn set theory on my own.
Thanks in advance
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A couple of ‘entry level’ treatments that can be confidently recommended.
Herbert B. Enderton, The Elements of Set Theory (Academic Press, 1997) is particularly clear in marking off the informal development of the theory of sets, cardinals, ordinals etc. (guided by the conception of sets as constructed in a cumulative hierarchy) and the formal axiomatization of ZFC. It is also particularly good and non-confusing about what is involved in (apparent) talk of classes which are too big to be sets – something that can mystify beginners. It is written with a certain lightness of touch and proofs are often presented in particularly well-signposted stages. The last couple of chapters or so perhaps do get a bit tougher, but overall this really is quite exemplary exposition.
Derek Goldrei, Classic Set Theory (Chapman & Hall/CRC 1996) is written by a staff tutor at the Open University in the UK and has the subtitle ‘For guided independent study’. It is as you might expect extremely clear, it is quite attractively written (as set theory books go!), and is indeed very well-structured for independent reading. The coverage is very similar to Enderton’s, and either book makes a fine introduction (but for what it is worth, I prefer Enderton ).
For more see entries on set theory in this Guide to reading on logic.
The best rigorous treatment that I’ve seen at the senior undergraduate/first-year graduate level is Karel Hrbacek & Thomas Jech, Introduction to Set Theory. The first edition was already very good, and the third has been expanded to include some important topics that were not originally covered. I agree with the very favorable Amazon review by Michael Greinecker (who also posts here at Math.SE).