I'm essentially looking for a book on set theory that would include material that begins to go deeper for a student who has/currently taken algebra, topology, and analysis undergrad courses.

Edit: I found Introduction to Axiomatic Set Theory through GTM, which hopefully seems to be what I'm looking for. Any other suggestions would be welcome.

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    $\begingroup$ See my comment here... $\endgroup$ – Asaf Karagila Mar 1 '18 at 16:37
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    $\begingroup$ I'll let one of MSE's hardcore set theorists post an actual answer, but two that come to my mind are Set Theory by Thomas Jech and Set Theory: An Introduction to Induction Proofs by Kenneth Kunen. $\endgroup$ – Clive Newstead Mar 1 '18 at 16:37
  • $\begingroup$ Very much appreciated! I'll look into these. $\endgroup$ – Good Morning Captain Mar 1 '18 at 16:44
  • $\begingroup$ The subtitle to Kunen's book is "an introduction to independence proofs" $\endgroup$ – Tim kinsella Mar 1 '18 at 17:21
  • $\begingroup$ I think Kunen's book is a little difficult if you have zero experience with set theory, and your mathematical background is "algebra, topology, and analysis undergrad courses." As is Jech's book. I would go with Introduction to set theory by Jech and Hrbacek. @CliveNewstead BTW the new edition of Kunen's book no longer has the subtitle, the subtitled book is very very old. Anyway, I don't think I'd start with Kunen, even though it is my favorite mathematics textbook. $\endgroup$ – JKEG Mar 3 '18 at 3:13

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