I am looking for books with set theory and logic that is sufficient to understand mathematical analysis. I guess another question might be if there even exists such a book.
There are basically two problems I have seen in real analysis that requires set theory. They often create very big sets, but in set theory you can't just create sets, you have to know why it is a set, in order to not get a paradox? The second thing from set theory that is often used is the axiom of choice and zorn's lemma.
Are there more things from set theory that is used in real analysis?(and also functional analysis)(apart from the operations of unions, intersections etc..)
Are there any books that gives a good(and hopefully easy) introduction to all that is needed of set-theory in mathematical analysis?