 One reason for concentrating on definable sets of reals is that it is generally easier to gain insight into definable sets of reals than arbitrary sets of reals and, furthermore, there is hope that this insight will shed light on the latter. For example, in one of the earliest results in the subject, Cantor and Bendixson showed that every closed set is either countable or has the size of the continuum; in other words, the closed sets satisfy CH. 