Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00153-007-0061-3
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dc.titleSchnorr trivial reals: A construction
dc.contributor.authorFranklin, J.N.Y.
dc.date.accessioned2016-11-16T11:06:30Z
dc.date.available2016-11-16T11:06:30Z
dc.date.issued2008-05
dc.identifier.citationFranklin, 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
dc.identifier.issn09335846
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/130487
dc.description.abstractA 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.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1007/s00153-007-0061-3
dc.sourceScopus
dc.subjectRandomness
dc.subjectSchnorr trivial
dc.subjectTriviality
dc.typeConference Paper
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1007/s00153-007-0061-3
dc.description.sourcetitleArchive for Mathematical Logic
dc.description.volume46
dc.description.issue7-8
dc.description.page665-678
dc.identifier.isiut000255112500009
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