Hey Prof Kim.
I was wondering if you know any good books in Set Theory? Well,I have been looking for one but i can’t really tell if they are any
It is somewhat important to be aware that you’ll find at least two different kinds of books on set theory that can confuse beginners with their superficially similar appearances. The kind that involves set theory at the research level, you might be interested in at some point, but I suspect it’s not quite what you’re looking for at the moment. Many such books can be studied in principle with no prerequisites, but actually assume a good deal of mathematical sophistication on the part of the reader. On the other hand, the kind that’s more important for the beginning undergraduate is a solid book that just teaches you the language of mathematics rigorously, while giving you at least a flavor of the deeper issues. For this, the book I myself studied from as a student was
Introduction to Set Theory by K. Hrbacek and T. Jech
It’s available in the UCL library. I remember feeling quite satisfied with their presentation.
As with other books in mathematics, it’s rather important to do all the exercises. If you have specific questions as you work through them, don’t hesitate to let me know.