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Currently i am studying undergraduate mathematics. My current understanding of set theory and logic comes from chapter 1 of Munkres' topology and from Rudin. I am of the opinion that this is not enough . I can see several loopholes in my understanding of several important lemmas and theorems . For example i have no understanding of continuum hypothesis and i don't fully understand the importance of choice function apart from that it makes certain recursions unique.

Should i read a book on formal mathematical logic ?Currently i have Peter Hinman's book on mathematical logic.

Disclaimer- i have serious shortage of time. I indeed to take a proper course on logic latter.

Bluey
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    Honestly, I think you can probably do ok with a less rigorous understanding of logic. Set theory on the other hand, you need to be more prepared for. – Rushabh Mehta Aug 18 '18 at 12:23
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    The continuum-hypothesis is a "big gun" of set theory as well as the axiom of choice. Both are independent from ZFC , hence neither true nor false. Fortunately, set theory is not really necessary to understand undergradutate mathematics. – Peter Aug 18 '18 at 12:25
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    Just understand how to use the axiom of choice, or equivalently Zorn's lemma. There is no need to understand the continuum hypothesis in any deep way (e.g., why it is undecidable). Beyond that, the level of set theory and logic in a book like Munkres is fine as background for any undergraduate (or many graduate) courses outside of courses on logic itself. – KCd Aug 18 '18 at 12:26
  • @RushabhMehta i have taken a course on discrete mathematics . That course was meant for CS majors . It has some set theory. – Bluey Aug 18 '18 at 12:30
  • @KCd ok thanks. – Bluey Aug 18 '18 at 12:30
  • @Peter thanks.. – Bluey Aug 18 '18 at 12:31
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    Recommendation: Work through part $1$ (pages $1$$-$$66$) of the text: Kaplansky -- Set Theory and Metric Spaces (1972). It's self-contained, and very well written. – quasi Aug 18 '18 at 12:40
  • @Peter I hope you realize ZFC is Zermelo Frankel $\textbf{with choice}$. So, obviously, ZFC is not independent from the Axiom of Choice – Rushabh Mehta Aug 18 '18 at 12:51
  • @RushabhMehta Thank you for pointing that out (in fact I did not notice) ! – Peter Aug 18 '18 at 12:52
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    I've done through a lot of graduate courses without any formal set theory. Zorn's lemma and choice is sufficient, in some cases Hausdorff maximal principle. I find Halmos' set theory to be enough for anyone not working formally with set theory or logic. – I was suspended for talking Aug 18 '18 at 14:23
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    I agree with the Kaplansky recommendation by @quasi (the book I learned the basics of set theory from). One of the things that somewhat bothered me at that time with the "naive" approach (also taken in Munkres) when the equivalences of Zorn's lemma and Axiom of Choice and Hausdorff's Maximality Principle are proved is that, since these are tools used in standard mathematics, exactly what is being proved? If I could go back in time and discuss this with my younger self, I would advise myself not to worry about this, but rather think of these proofs as examples of how to apply these tools. – Dave L. Renfro Aug 18 '18 at 16:50

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