Source: J. Symbolic Logic
Volume 71, Issue 3
We prove that there exists a noncomputable c.e. real which is low for
weak 2-randomness, a definition of randomness due to Kurtz, and that all
reals which are low for weak 2-randomness are low for Martin-Löf
Full-text: Access denied (no subscription
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
R. Downey, E. Griffiths, and S. Reid, On Kurtz randomness, Theoretical Computer Science, vol. 321 (2004), pp. 249--270.
R. Downey and D. Hirschfeldt Algorithmic Randomness and Complexity, Springer-Verlag, to appear. Current version available at http://www.mcs.vuw.ac.nz/~downey.,
S. Figueira, A. Nies, and F. Stephan, Lowness properties and approximations of the jump, Proceedings of the Workshop of Logic, Language, Information and Computation (WoLLIC), 2005, Electronic Lecture Notes in Theoretical Computer Science, vol. 143(2006), pp. 45--57.
P. Gács, Every set is reducible to a random one, Information and Control, vol. 70 (1986), pp. 186--192.
Mathematical Reviews (MathSciNet): MR859105
H. Gaifman and M. Snir, Probabilities over rich languages, testing and randomness, Journal of Symbolic Logic, vol. 47 (1982), pp. 495--548.
Mathematical Reviews (MathSciNet): MR666815
S. Kautz Degrees of random sets, Ph.D. thesis, Cornell University, 1991.,
S. Kurtz Randomness and genericity in the degrees of unsolvability, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1981.,
A. Kučera, Measure, $\Pi^0_1$ classes, and complete extensions of PA, Lecture Notes in Mathematics, vol. 1141, Springer, 1985, pp. 245--259.
Mathematical Reviews (MathSciNet): MR820784
A. Kučera and S. Terwijn, Lowness for the class of random sets, Journal of Symbolic Logic, vol. 64 (1999), no. 4, pp. 1396--1402.
P. Martin-Löf, The definition of random sequences, Information and Control, vol. 9 (1966), pp. 602--619.
Mathematical Reviews (MathSciNet): MR223179
A. Nies Computability and Randomness, to appear.,
--------, Low for random sets: The story, preprint, available at http://www.cs.auckland.ac.nz/% nies.
--------, Non-cupping and randomness, Proceedings of the American Mathematical Society, to appear.
G. Sacks Degrees of Unsolvability, Princeton University Press, 1963.,
Mathematical Reviews (MathSciNet): MR186554
F. Stephan personal communication.,
Y. Wang Randomness and Complexity, Ph.D. thesis, University of Heidelberg, 1996.,