Randomness, relativization and Turing degrees

@article{Nies2005RandomnessRA,
  title={Randomness, relativization and Turing degrees},
  author={Andr{\'e} Nies and Frank Stephan and Sebastiaan Terwijn},
  journal={J. Symb. Log.},
  year={2005},
  volume={70},
  pages={515-535}
}
We compare various notions of algorithmic randomness. First we consider relativized randomness. A set is ?-random if it is Martin-L?f random relative to 0_1). We show that a set is 2-random if and only if there is a constant c such that infinitely many initial segments x of the set are c-incompressible: C(x) > |x| ? c. The 'only if direction was obtained independently by Joseph Miller. This characterization can be extended to the case of time-bounded C -complexity. Next we prove some results on… CONTINUE READING

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