A weakly 2-random set that is not generalized low

Lewis-Pye, A., Montalbán, A. & Nies, A. (2007). A weakly 2-random set that is not generalized low. In Cooper, S. B., Löwe, B. & Sorbi, A. (Eds.), Computation and Logic in the Real World: Third Conference on Computability in Europe, Cie 2007, Siena, Italy, June 18-23, 2007 (pp. 474-477). Springer Berlin / Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_49
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A guiding question in the study of weak 2-randomness is whether weak 2-randomness is closer to 1-randomness, or closer to 2-randomness. Recent research indicates that the first alternative holds. We add further evidence in this direction by showing that, in contrast to the case for 2-randomness, a weakly 2-random set can fail to be generalized low.

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