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I finished some elementary proof-writing courses, but I am not quite familiar with mathematical logic and set theory yet. Can you recommend some books that cover set theory and mathematical logic in one book?

Your recommendations about books on set theory or mathematical logic alone will be appreciated, though.

Shaun
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SU Lee
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    I think Naive Set Theory (by Halmos) is a very good treatment of the basics of set theory. It is short and still contains more then you need. How ever it does not really contain exercises. The entire book is an exercise, and it wonderfully written. It does not really contain "mathematical logic", but I am not sure what you really mean with that, as "logic" is an area of mathematics. Also you might want to look at Hammack's Book of Proof. It is a very good introduction to mathematics overall, and I guess you should find everything there you need to get started. It is freely available. – Cornman Feb 04 '22 at 22:54
  • @Cornman Thanks! I liked the linear algebra book by Halmos, so I think it would be nice too. – SU Lee Feb 04 '22 at 23:08
  • If you already had Linear Algebra, I do not think that you benefit from Halmos book. But you can take a look and judge for yourself. – Cornman Feb 04 '22 at 23:10
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    I think the problem is that you can do a lot of basic set theory without going into formal logic, and texts that combine both areas will therefore be usually more advanced. Three such books would be "The Foundations of Mathematics" by Kunen, "Logic, Induction and Sets" by Forster, and "Notes on Logic and Set Theory" by Johnstone. All great books, but all probably more advanced than what you are looking for. – Michael Greinecker Feb 04 '22 at 23:28
  • There MAY be better uses of your time if you want to specialize in say analysis or algebra. Ask around. – Dan Christensen Feb 05 '22 at 02:22
  • @MichaelGreinecker Thanks! I will find them out! – SU Lee Feb 05 '22 at 02:28
  • @DanChristensen In fact, I am studying a proof assistant, in which mathematical logic seems to be very important (I am not sure though). – SU Lee Feb 05 '22 at 02:32
  • If your goal is a proof assistant, then it would be better to dive into relevant stuff (like guides for Coq or Lean), learn a modicum of mathematical logic (set theory is not necessary), and ask questions to people studying programming language theory. Also, the theoretical CS.SE would be a better place for your study. – Hanul Jeon Feb 05 '22 at 09:07

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The Open Logic Project has some books on logic and set theory. They're all free and open source.

There are also some questions on the site that cover half your question.

For example, this decade-old question lists books on mathematical logic, but doesn't say which ones also cover set theory.

Greg Nisbet
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For an extensive guide, with book recommendations at various levels, see the freely downloadable Beginning Mathematical Logic: A Study Guide

Peter Smith
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