Rank and Randomness

  title={Rank and Randomness},
  author={R. H{\"o}lzl and Christopher P. Porter},
  journal={J. Symb. Log.},
  • R. Hölzl, Christopher P. Porter
  • 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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