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I am an engineering and applied math undergraduate and I like reading up on the pure math behind what I study in my nonexistent free time. I’m taking probability soon and would like to supplement it by starting to read some set theory. From scouring previous posts, it seems that two names that pop up repeatedly are Halmos’ Naive Set Theory and and Jech’s Set Theory. I used to have a “one book” mindset, trying to find “the book” for every subject, but quickly realized this to be very limiting to my understanding, so I’ve upped myself to “the two books”, and these two, in that order, seem good for introduction (Halmos) and then getting in the weeds a bit more(Jech). Is this a good assessment/approach? I’ve only done a proof-based linear algebra course along with diffeq for my undergraduate math, to give an idea of where I’m at. I would love to hear about other ideas/recommendations if you have them.

Thanks,

—-D.R.

P.S. You pure math people are awesome for comprehending these subjects so quickly. I could imagine getting through these books in the space of a semester or two.

RD Healthcare
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    Does this answer your question? Textbooks on set theory (Jech might be too advanced given your background) – David M Mar 14 '24 at 04:57
  • A bit, but there are enough suggestions to not be sure of any specific one (I’m also indecisive). That’s one of the posts I used to develop this post. I’ll be going through Linear Algebra done right, Tao’s Analysis, and a Calculus 3 course before attempting this. I don’t have a good sense of where my mathematical maturity is but haven’t run into too much trouble with these texts. Would a different book either be a better replacement or intermediate step for Jech? – RD Healthcare Mar 14 '24 at 13:25
  • To add to this, between Halmos and Jech or whatever follows Halmos, might it be beneficial to study some mathematical logic? If so, I’ll make a separate post about that. – RD Healthcare Mar 14 '24 at 13:39
  • It's an age old debate - plenty of posts here about it - whether to start with logic or with set theory. Jech is really advanced, more of a reference book. Drake, Intermediate Set Theory has a lot of fans, and would be a good book after Halmos and before Jech. Also covers some logic if I recall. – David M Mar 14 '24 at 14:46
  • Got it. I’ll check those out. – RD Healthcare Mar 15 '24 at 05:43
  • Another great intermediate book is Nik Weaver, Forcing for Mathematicians, written more from the point of view of "set theory for mathematicians" rather than "set theory for set theorists". – David M Mar 15 '24 at 05:52
  • Is there one after Halmos that stands out as being the most comprehensive? I don’t mind difficulty or terseness as long as the information in the book doesn’t have actual prerequisite information I’d need to understand. – RD Healthcare Mar 15 '24 at 17:11
  • As far as I recall, Jech is actually self contained, and it will most likely be by far the most comprehensive. – David M Mar 16 '24 at 04:00
  • I would recommand to you that you check out Hammack's book (it is free): https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf It contains everything you need to know to start mathematics. – Cornman Mar 19 '24 at 16:05

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