Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424810 | Annals of Pure and Applied Logic | 2014 | 17 Pages |
Abstract
Let f be a computable function from finite sequences of 0ʼs and 1ʼs to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that f-randomness relative to a PA-degree implies strong f-randomness, hence f-randomness does not imply f-randomness relative to a PA-degree.
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
Kojiro Higuchi, W.M. Phillip Hudelson, Stephen G. Simpson, Keita Yokoyama,