Given that I am going through Munkres's book on topology , I had to give a glance at the topics included in the first chapter like that of Axiom of choice, The maximum principle, the equivalence of the former and the later etc. Given all this I doubt that I know enough of set theory , or more precisely and suiting to my business , Lack a good deal of rigor in my ingredients. I wanted to know whether research is conducted on set theory as an independent branch. Is there any book that covers all about set theory, like the axioms, the axiom of choice and other advanced topics in it. I have heard about the Bourbaki book, but am helpless at getting any soft copy of that book.
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Here are four suggestions (two "entry level" books, and two just a notch up in difficulty):
All these books are in print, though none are cheap: indeed, Enderton’s is quite absurdly expensive. But all are ‘musts’ for any university library and are widely available. I’d strongly advise reading one of the first pair and then one of the second pair. (And do this before tackling more advanced books like Kunen's or the Jech bible which go more a lot more quickly through the basics and then deal with more advanced topics including forcing and large cardinals.)
I'd recommend "Naive Set Theory" by Halmos. It is a fun read, in a leisurely style, starts from the axioms and prove the Axiom of Choice.
Also, see this XKCD. http://xkcd.com/982/