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A set of infinite binary sequences C⊆2^ω is negligible if there is no partial probabilistic algorithm that produces an element of this set with positive probability. The study of negligibility is of particular interest in the context of Π^0_1 classes. In this paper, we introduce the notion of depth for Π^0_1 classes, which is a stronger form of negligibility. Whereas a negligible Π^0_1 class C has the property that one cannot probabilistically compute a member of C with positive probability, aarXiv:1403.0450v3 fatcat:i63bvw7llnhodbdw6tn5sjcswq