Computational Randomness and Lowness

@article{Terwijn2001ComputationalRA,
  title={Computational Randomness and Lowness},
  author={Sebastiaan Terwijn and Domenico Zambella},
  journal={J. Symb. Log.},
  year={2001},
  volume={66},
  pages={1199-1205}
}
We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0 0. This contrasts with a result of Ku cera and Terwijn 5] on sets that are low for the class of Martin-LL of random reals. The Cantor space 2 ! is the set of innnite binary sequences; these are called reals and are identiied with subsets of !. If 2 2 <! , that is, is a… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-8 of 8 references

Mayordomo,Resource-bounded measure and ran- domness

E. K. Ambos-Spies
1997
View 1 Excerpt

Classical recursion theory

P. Odifreddi
North-Holland • 1989

A mathematical proof of S

J. Raisonnier
Shelah's theorem on the mea- sure problem and related results. Israel J. Math. 48 • 1984
View 1 Excerpt

Measure, 01-classes, and complete extensions of PA, in: H.

A. Ku cera
Recursion The- ory Week • 1984
View 1 Excerpt

The degrees of hyperimmune sets

W. Miller, D. A. Martin
Z. Math. Logik Grundlagen Math. 14 • 1968
View 1 Excerpt

The de nition of random sequences, Information and Control

P. Martin-Lof
1966
View 1 Excerpt

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