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RANK AND RANDOMNESS

Published online by Cambridge University Press:  19 September 2019

RUPERT HÖLZL
Affiliation:
INSTITUT 1, FAKULTÄT FÜR INFORMATIK UNIVERSITÄT DER BUNDESWEHR MÜNCHEN WERNER-HEISENBERG-WEG 39, 85579, NEUBIBERG, GERMANY E-mail: r@hoelzl.frURL: http://hoelzl.fr
CHRISTOPHER P. PORTER
Affiliation:
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE DRAKE UNIVERSITY DES MOINES, IA50311, USA E-mail: cp@cpporter.comURL: http://cpporter.com

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.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2019 

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