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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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    I don't think Bourbaki is where you should start learning set theory ^^2012-12-23
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    Karel Hrbacek & Thomas Jech, [*Introduction to Set Theory*](http://www.amazon.com/Introduction-Revised-Expanded-Chapman-Mathematics/dp/0824779150) is a good introductory text at the senior undergraduate or first-year graduate level. It may be a bit too advanced, but you won’t find a good treatment of all of the topics that you mentioned at a much lower level.2012-12-23
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    @BrianM.Scott Any such book having an available PDF version . Sir, How about your lecture notes?2012-12-23
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    Other quite comprehensive books are Jech's Set Theory and Kenneth Kunen's Set theory: introduction to independence proofs. But those may be a little too fast-paced for a beginner... I'm pretty sure all these books have pdf versions, if you know where to look. Out of curiosity, what is this thing you call maximum principle?2012-12-23
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    @tomasz: Those are definitely too hard for someone who’s having some trouble with Munkres. Presumably the maximum principle is the [Hausdorff maximum principle](http://en.wikipedia.org/wiki/Hausdorff_maximal_principle).2012-12-23
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    I am in a relatively similar position (just starting to look at set theory). I got Set Theory by Jech which is a pretty large volume but it covers a lot of material. I am using it in conjunction with other books and the internet but I find it very useful. It is however £100 new (I got mine out of my library :) )2012-12-23
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    Judy Roitman’s *Introduction to Modern Set Theory* is available [here](http://www.math.ku.edu/~roitman/) as a PDF. In principle it’s intended for the same audience as Hrbacek & Jech, but I’d rate it a little more difficult.2012-12-23
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    The appendix of John L. Kelley's book *General Topology* has an extremely concise and clear development of axiomatic set theory. That is what first got me interested in the subject.2012-12-24
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    There are two questions here that need separating. That first chapter of Munkres has most of the set theory you need in order _to do non-set theory math_. If this is what you want, I'd read Halmos and work through that part of Munkres, then study other things. If you're interested in set theory _as a field of study_, Jech and the other advanced references mentioned are what you want. But you won't need to read Jech to do e.g. algebraic geometry.2012-12-24

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