Author:
BIENVENU LAURENT,DOWNEY ROD,GREENBERG NOAM,NIES ANDRÉ,TURETSKY DAN
Abstract
AbstractWe show the existence of noncomputable oracles which are low for Demuth randomness, answering a question in [15] (also Problem 5.5.19 in [34]). We fully characterize lowness for Demuth randomness using an appropriate notion of traceability. Central to this characterization is a partial relativization of Demuth randomness, which may be more natural than the fully relativized version. We also show that an oracle is low for weak Demuth randomness if and only if it is computable.
Publisher
Cambridge University Press (CUP)
Reference39 articles.
1. Randomness and lowness notions via open covers
2. [10] Diamondstone D. , Greenberg N. , and Turetsky D. , Inherent enumerability of strong jump-traceability . Transactions of the American Mathematical Society, to appear.
3. [29] Kučera A. and Nies A. , Demuth’s path to randomness (extended abstract). Computation, physics and beyond. Lecture Notes in Computer Science, vol. 7160, pp. 159–173, 2012.
4. Randomness notions and partial relativization
5. An alternative, priority-free, solution to Post's problem
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