Lowness and \(\Pi^0_2\) nullsets. (English) Zbl 1112.03040

The authors prove two results: a) the existence of a noncomputable c.e. real which is low for weak 2-randomness; b) all reals low for weak 2-randomness are low for 1-randomness.


03D80 Applications of computability and recursion theory
68Q30 Algorithmic information theory (Kolmogorov complexity, etc.)
03D25 Recursively (computably) enumerable sets and degrees
Full Text: DOI


[1] DOI: 10.1016/S0019-9958(86)80004-3 · Zbl 0628.03024
[2] DOI: 10.1016/S0019-9958(66)80018-9 · Zbl 0244.62008
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[10] Algorithmic Randomness and Complexity · Zbl 1221.68005
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