A Cantor-Bendixson-like process which detects Delta_2^0

For each subset of Baire space, we define, in away similar to a common proof of the Cantor-Bendixson Theorem, a sequence of decreasing subsets S_alpha of N^N, indexed by ordinals. We use this to obtain two new characterizations of the boldface Delta_2^0 Borel pointclass. ADDENDUM: In January 2012 we learned that the notion of guessability appeared in an equivalent form, and even with the same name, in the doctoral dissertation of William Wadge [4]. As for the main result of this paper, Wadge proved one direction and gave a proof for the other direction which he attributed to Hausdorff. The proofs in this paper present an alternate means to those results.