Rank and randomness

Journal of Symbolic Logic 84 (4):1527-1543 (2019)
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Abstract

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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Christopher Porter
Drake University

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