RANK AND RANDOMNESS.
We show that for each computable ordinal $\alpha > 0$ it is possible to find in each Martin-Löf random ${\rm{\Delta }}_2^0 $ degree a sequence R of Cantor-Bendixson rank α , while ensuring that the sequences that inductively witness R 's rank are all Martin-Löf random with respect to a single coun...
| Published in: | Journal of Symbolic Logic Vol. 84; no. 4; pp. 1527 - 1544 |
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| Main Authors: | , |
| Format: | Article |
| Published: |
Cambridge University Press
Dec2019
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| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| Summary: | We show that for each computable ordinal $\alpha > 0$ it is possible to find in each Martin-Löf random ${\rm{\Delta }}_2^0 $ degree a sequence R of Cantor-Bendixson rank α , while ensuring that the sequences that inductively witness R 's rank are all Martin-Löf random with respect to a single countably supported and computable measure. This is a strengthening for random degrees of a recent result of Downey, Wu, and Yang, and can be understood as a randomized version of it. |
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