English

Rank and randomness

Logic 2020-02-19 v3

Abstract

We show that for each computable ordinal α>0\alpha>0 it is possible to find in each Martin-L\"of random Δ20\Delta^0_2 degree a sequence RR of Cantor-Bendixson rank α\alpha, while ensuring that the sequences that inductively witness RR'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.

Keywords

Cite

@article{arxiv.1707.00378,
  title  = {Rank and randomness},
  author = {Rupert Hölzl and Christopher P. Porter},
  journal= {arXiv preprint arXiv:1707.00378},
  year   = {2020}
}
R2 v1 2026-06-22T20:35:48.355Z