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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.

MSC:

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

[1] DOI: 10.1016/S0019-9958(86)80004-3 · Zbl 0628.03024
[2] DOI: 10.1016/S0019-9958(66)80018-9 · Zbl 0244.62008
[3] Probabilities over rich languages, testing and randomness 47 pp 495– (1982)
[4] Proceedings of the Workshop of Logic, Language, Information and Computation (WoLLIC), 2005 143 pp 45– (2006)
[5] Measure, classes, and complete extensions of PA 1141 pp 245– (1985)
[6] DOI: 10.1016/j.tcs.2004.03.055 · Zbl 1070.68054
[7] Degrees of Unsolvability (1963) · Zbl 0143.25302
[8] Proceedings of the American Mathematical Society
[9] Lowness for the class of random sets 64 pp 1396– (1999) · Zbl 0954.68080
[10] Algorithmic Randomness and Complexity · Zbl 1221.68005
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