CONSTRUCTING WADGE CLASSES

Abstract We show that, assuming the Axiom of Determinacy, every non-selfdual Wadge class can be constructed by starting with those level $\omega _1$ (that is, ones that are closed under Borel preimages) and iteratively applying operations expansion separated differences. The proof is essentially due to Louveau, it yields at same time a new theorem Van Wesep (namely, expressed as result Hausdorff operation applied open sets). exposition self-contained, except for facts from classical descriptive set theory.