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arXiv · 1707.00378

Rank and randomness

Rupert Hölzl·Christopher P. Porter
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Abstract

We show that for each computable ordinal $α>0$ it is possible to find in each Martin-Löf random $Δ^0_2$ 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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BibTeXRIS

Rupert Hölzl, Christopher P. Porter. 2019-10-09. Rank and randomness. https://doi.org/10.1017/jsl.2019.65

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