Prompt enumerations and relative randomness
type: Item
instance of: scholarly article
title: Prompt enumerations and relative randomness
zbMATH Open document ID: 1256.03047
author: Anthony Morphett
publication date: 2012-09-05T00:00:00Z
Mathematics Subject Classification ID: 03D32
Mathematics Subject Classification ID: 03D25
zbMATH DE Number: 6078054
zbMATH Keywords: c.e. degrees
zbMATH Keywords: promptness
zbMATH Keywords: prompt simplicity
zbMATH Keywords: relative randomness
MaRDI profile type: Publication
full work available at URL: exq049
OpenAlex ID: W2150399145
DOI: 10.1093/LOGCOM/EXQ049
published in: Journal of Logic and Computation
review text: In the paper under review a notion of prompt non-low-for-randomness is introduced. It is analogous to the property of prompt simplicity and to the equivalent property of prompt permitting. The introduced property is a prompt form of non-low-for-random permitting, which is the natural notion of permitting in the context of relative randomness. It is shown that the class of Turing degrees of promptly non-low-for-random c.e. sets is non-trivial and a proper subclass of the non-low-for-random promptly simple degrees. The prompt non-low-for-randomness is also considered in the context of the LR-degrees and LR-reducibility, a weak reducibility arising naturally from relative randomness.
reviewed by: Roman Murawski
description: scientific article; zbMATH DE number 6078054