A friend of mine has asked for a reference to a resource for self study of set theory (for the sake of it). He has knowledge of basic predicate logic.

The books I know of are not suited for a non-mathematician, because even if they assume no prior knowledge, they are written in very technical fashion. Video series I know of (i.e. youtube videos) tend to be too superficial.

Any suggestions?

Edit: As (rightly) suggested in the comments, I'll expand a bit: I think a good book or lecture would be one that includes an introduction to the basic naive stuff (cardinals, ordinals, AC and it's equivalences). As well as nice "showcase" of results from these ideas (i.e. $|\mathbb{R}|=2^{\aleph_0}>\aleph_0=|\mathbb{N}|$).

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    $\begingroup$ Not to tout my own horn, but... this might be useful. $\endgroup$ – Asaf Karagila Feb 28 '18 at 17:10
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    $\begingroup$ it comes to my mind Naive set theory of Halmos. $\endgroup$ – Masacroso Feb 28 '18 at 17:12
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    $\begingroup$ Perhaps this one (at least it's free): math.ku.edu/~roitman/SetTheory.pdf If that's too technical, then perhaps start with a chapter on set theory from a standard Discrete Math text. $\endgroup$ – quasi Feb 28 '18 at 17:18
  • $\begingroup$ @Masacroso: What a terrible book. :( $\endgroup$ – Asaf Karagila Feb 28 '18 at 17:19
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    $\begingroup$ @j3M: Kaplansky's book covers cardinals, ordinals, the axiom of choice, all at the naive level, but still rigorous. And in my opinion, all of Kaplansky's books are very well written. $\endgroup$ – quasi Feb 28 '18 at 17:40

Your friend might be interested in

Sets, logic, and axiomatic theories / by Robert R. Stoll | 1961

The first chapter should be accessible to your friend:

enter image description here

The book can be checked out online from the Internet Archive.

It should be pointed out that the world wide web is an incredible resource. Using search engines your friend could find relevant links by looking for keywords found in Stoll's Chapter 1. For example, use duckduckgo.com on

sets ordering relations math

If your friend is interested "in cardinals, ordinals, AC and it's equivalences... and 'showcase' of results from these ideas (i.e. $|\mathbb{R}|=2^{\aleph_0}>\aleph_0=|\mathbb{N}|$)", you should point them towards this site!

Interested in learning about cardinals? Could not find a duckduckgo bang, but this works,

cardinals site:www.math.stackexchange.com


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