# Rank and Randomness

@article{Hlzl2019RankAR,
title={Rank and Randomness},
author={R. H{\"o}lzl and Christopher P. Porter},
journal={J. Symb. Log.},
year={2019},
volume={84},
pages={1527-1543}
}
• Published 2019
• Computer Science, Mathematics
• J. Symb. Log.
• We show that for each computable ordinal $\alpha>0$ it is possible to find in each Martin-L\"of random $\Delta^0_2$ degree a sequence $R$ of Cantor-Bendixson rank $\alpha$, while ensuring that the sequences that inductively witness $R$'s rank are all Martin-L\"of 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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