Kjos-Hanssen, Bjørn Low for random reals and positive-measure domination. (English) Zbl 1128.03031 Proc. Am. Math. Soc. 135, No. 11, 3703-3709 (2007). The low for random reals are characterised topologically and in terms of domination of Turing functionals on a set of positive measure. Reviewer: Cristian S. Calude (Auckland) Cited in 3 ReviewsCited in 19 Documents MSC: 03D28 Other Turing degree structures 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.) PDFBibTeX XMLCite \textit{B. Kjos-Hanssen}, Proc. Am. Math. Soc. 135, No. 11, 3703--3709 (2007; Zbl 1128.03031) Full Text: DOI arXiv References: [1] Bjørn Kjos-Hanssen, André Nies, and Frank Stephan, Lowness for the class of Schnorr random reals, SIAM J. Comput. 35 (2005), no. 3, 647 – 657. · Zbl 1095.68043 [2] S. Binns, B. Kjos-Hanssen, M. Lerman, and D.R. Solomon, On a question of Dobrinen and Simpson concerning almost everywhere domination, J. Symbolic Logic 71 (2006), no. 1, 119-136. · Zbl 1103.03014 [3] Gregory J. Chaitin, A theory of program size formally identical to information theory, J. Assoc. Comput. Mach. 22 (1975), 329 – 340. · Zbl 0309.68045 [4] Peter Cholak, Noam Greenberg, and Joseph S. Miller, Uniform almost everywhere domination, J. Symbolic Logic 71 (2006), no. 3, 1057 – 1072. · Zbl 1109.03034 [5] Natasha L. Dobrinen and Stephen G. Simpson, Almost everywhere domination, J. Symbolic Logic 69 (2004), no. 3, 914 – 922. · Zbl 1075.03021 [6] D.R. Hirschfeldt, A. Nies, and F. Stephan, Using random sets as oracles, to appear. · Zbl 1128.03036 [7] Antonín Kučera, Measure, \Pi \(^{0}\)\(_{1}\)-classes and complete extensions of \?\?, Recursion theory week (Oberwolfach, 1984) Lecture Notes in Math., vol. 1141, Springer, Berlin, 1985, pp. 245 – 259. · Zbl 0622.03031 [8] S.A. Kurtz, Randomness and genericity in the degrees of unsolvability, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1981, pp. VII+131 pages. [9] A. Nies, Low for random reals: the story, unpublished. [10] André Nies, Lowness properties and randomness, Adv. Math. 197 (2005), no. 1, 274 – 305. · Zbl 1141.03017 [11] André Nies, Frank Stephan, and Sebastiaan A. Terwijn, Randomness, relativization and Turing degrees, J. Symbolic Logic 70 (2005), no. 2, 515 – 535. · Zbl 1090.03013 [12] C.-P. Schnorr, A unified approach to the definition of random sequences, Math. Systems Theory 5 (1971), 246 – 258. · Zbl 0227.62005 [13] Sebastiaan A. Terwijn and Domenico Zambella, Computational randomness and lowness, J. Symbolic Logic 66 (2001), no. 3, 1199 – 1205. · Zbl 0990.03033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.