 Thus a boldface pointclass is a downward-closed union of Wadge degrees.The Borel and projective hierarchies have analogs in effective descriptive set theory in which the definability property is no longer relativized to an oracle, but is made absolute.For example, if one fixes some collection of basic open neighborhoods (say, in Baire space, the collection of sets of the form {"x"∈ωω|"s" is an initial segment of "x"} for each fixed finite sequence "s" of natural numbers), then the open, or formula_1, sets may be characterized as all (arbitrary) unions of basic open neighborhoods.