We systematically compare ω -Boolean classes and Wadge classes, e.g. we complement the result of W. Wadge that the collection of non-self-dual levels of his hierarchy coincides with the collection of classes generated by Borel ω -ary Boolean operations from the open sets in the Baire space. Namely, we characterize the operations, which generate any given level in this way, in terms of the Wadge hierarchy in the Scott domain. As a corollary we deduce the non-collapse of the latter hierarchy. Also, the effective version of this topic is developed.