I have learned that set of all dedekind cut has properties of real number we know.
How do i know whether the set of all cuts is stronger than real number? i.e. set of all dedekind cuts may have a property P, which real number we know doesn't have.
Let A be a set of all dedekind cuts of $Q$. Let B be a set of all cuts of A. I heard that B has exactly the same property of A, thus A and B both can be viewed as real number. Please suggest me any book or sites i can study this..