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|Title:||Schnorr trivial reals: A construction||Authors:||Franklin, J.N.Y.||Keywords:||Randomness
|Issue Date:||May-2008||Citation:||Franklin, J.N.Y. (2008-05). Schnorr trivial reals: A construction. Archive for Mathematical Logic 46 (7-8) : 665-678. ScholarBank@NUS Repository. https://doi.org/10.1007/s00153-007-0061-3||Abstract:||A real is Martin-Löf (Schnorr) random if it does not belong to any effectively presented null σ0 2 (recursive) class of reals. Although these randomness notions are very closely related, the set of Turing degrees containing reals that are K-trivial has very different properties from the set of Turing degrees that are Schnorr trivial. Nies proved in (Adv Math 197(1):274-305, 2005) that all K-trivial reals are low. In this paper, we prove that if bf h'} ≥T bf 0', then h contains a Schnorr trivial real. Since this concept appears to separate computational complexity from computational strength, it suggests that Schnorr trivial reals should be considered in a structure other than the Turing degrees. © 2007 Springer-Verlag.||Source Title:||Archive for Mathematical Logic||URI:||http://scholarbank.nus.edu.sg/handle/10635/130487||ISSN:||09335846||DOI:||10.1007/s00153-007-0061-3|
|Appears in Collections:||Staff Publications|
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