Classification of the spaces Cp⁎(X) within the Borel-Wadge hierarchy for a projective space X

We provide a positive answer, i.e. assuming PD we prove, that if n≥2 and if X is a separable metrizable space which is in Σn1 but not in Σn−11, then the measurable space Cp⁎(X) is Borel-Πn1-complete. This completes under the assumption of PD the classification of Borel-Wadge complexity of Cp⁎(X) for X projective.