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CHARACTERIZING LOWNESS FOR DEMUTH RANDOMNESS

Published online by Cambridge University Press:  25 June 2014

LAURENT BIENVENU ,
ROD DOWNEY ,
NOAM GREENBERG ,
ANDRÉ NIES  and
DAN TURETSKY
LAURENT BIENVENU
Affiliation:
LIAFA, CNRS & UNIVERSITY OF PARIS 7 PARIS, FRANCEE-mail: laurent.bienvenu@liafa.univ-paris-diderot.fr
ROD DOWNEY
Affiliation:
SCHOOL OF MATHEMATICS, STATISTICS AND OPERATIONS RESEARCH VICTORIA UNIVERSITY OF WELLINGTON WELLINGTON, NEW ZEALANDE-mail: downey@msor.vuw.az.nz
NOAM GREENBERG
Affiliation:
SCHOOL OF MATHEMATICS, STATISTICS AND OPERATIONS RESEARCH VICTORIA UNIVERSITY OF WELLINGTON WELLINGTON, NEW ZEALANDE-mail: greenberg@msor.vuw.az.nz
ANDRÉ NIES
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF AUCKLAND, PRIVATE BAG 92019 AUCKLAND, NEW ZEALANDE-mail: andre@cs.auckland.ac.nz
DAN TURETSKY
Affiliation:
KURT GÖDEL RESEARCH FOR MATHEMATICAL LOGIC UNIVERSITY OF VIENNA VIENNA, AUSTRIAE-mail: turetsd4@univie.ac.at
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Abstract

We show the existence of noncomputable oracles which are low for Demuth randomness, answering a question in [15] (also Problem 5.5.19 in [34]). We fully characterize lowness for Demuth randomness using an appropriate notion of traceability. Central to this characterization is a partial relativization of Demuth randomness, which may be more natural than the fully relativized version. We also show that an oracle is low for weak Demuth randomness if and only if it is computable.

Keywords

Primary: 03D28 and 68Q30Secondary: 03D25Demuth randomnesspartial relativizationlowness
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 2 , June 2014 , pp. 526 - 560
Copyright
Copyright © The Association for Symbolic Logic 2014 

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