Please use this identifier to cite or link to this item: https://doi.org/10.1007/s11856-008-1019-9
Title: Lowness of higher randomness notions
Authors: Chong, C.T. 
Nies, A.
Yu, L.
Issue Date: Aug-2008
Citation: Chong, C.T., Nies, A., Yu, L. (2008-08). Lowness of higher randomness notions. Israel Journal of Mathematics 166 : 39-60. ScholarBank@NUS Repository. https://doi.org/10.1007/s11856-008-1019-9
Abstract: We study randomness notions given by higher recursion theory, establishing the relationships Π1 1 -randomness ⊂ Π1 1-Martin-Löf randomness ⊂ Δ1 1-randomness = Δ1 1-Martin-Löf randomness. We characterize the set of reals that are low for Δ1 1 randomness as precisely those that are Δ1 1-traceable. We prove that there is a perfect set of such reals. © 2008 Hebrew University Magnes Press.
Source Title: Israel Journal of Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103523
ISSN: 00212172
DOI: 10.1007/s11856-008-1019-9
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