# Looking for a book on set theory that covers cardinals, proper classes, extensions of ZFC etc. in detail

I'm fine with "naive" set theory and low level mathematical logic, however I want to understand set theory in particular at a deeper and more formal level. I want to learn more about cardinals as well as other higher order sets and about proper classes and formally handling them. It would be nice if the book had a formal definition of ZFC and also talked about maybe a few other popular extensions of ZFC like NGB or something. I know anything like this is going to require some more advanced mathematical logic that I may not have, so its fine if it has to go over that in some detail. However I want to try and maximize the ratio of set theory to mathematical logic as much as possible. Now I'm not sure where to start looking so if anyone experienced in these subjects could recommend a book to me, I'd be very grateful.

• @Asaf Karagila If you have any advice please, I'd appreciate anything. – user3865123 Apr 28 '18 at 21:14
• Jech.${}{}{}{}$ – Asaf Karagila Apr 28 '18 at 21:14
• @AsafKaragila logic.wikischolars.columbia.edu/file/view/…? It looks very good though I want to be sure I'm getting the book you are referring to. – user3865123 Apr 28 '18 at 21:16
• Yeah, that one. – Asaf Karagila Apr 28 '18 at 21:16
• @AsafKaragila Thanks, if you post the word Jech as an answer I'll accept it =) – user3865123 Apr 28 '18 at 21:17