Isolation and the high/low hierarchy
type: Item
instance of: scholarly article
title: Isolation and the high/low hierarchy
zbMATH Open document ID: 1028.03035
author: Guohua Wu
author: Sh. T. Ishmukhametov
published in: Archive for Mathematical Logic
publication date: 2003-09-16T00:00:00Z
review text: A subset \(D\) of \(\omega\) is called a d.c.e. (difference of c.e. sets) if there are c.e. (computably enumerable) sets \(A_0\) and \(A_1\) such that \(D=A_0 -A_1\). A d.c.e. degree \(\mathbf d\) is called isolated by a c.e. degree \(\mathbf b\) if \({\mathbf b}<{\mathbf d}\) and any c.e. degree \(\mathbf c\) below \(\mathbf d\) is also below \(\mathbf b\). The second author, \textit{Guohua Wu}, proved that there is a high d.c.e. degree \(\mathbf d\) isolated by a low\(_2\) c.e. degree \(\mathbf b\) [Math. Log. Q. 47, 525-534 (2001; Zbl 1003.03039)]. In this paper, the authors improve Wu's result and show that there are a high d.c.e. degree \(\mathbf d\) and a low c.e. degree \(\mathbf a\) such that \(\mathbf d\) is isolated by \(\mathbf a\).
reviewed by: Ning Zhong
Mathematics Subject Classification ID: 03D25
Mathematics Subject Classification ID: 03D30
zbMATH DE Number: 1982474
zbMATH Keywords: computably enumerable sets
zbMATH Keywords: difference of c.e. sets
zbMATH Keywords: d.c.e. degrees
zbMATH Keywords: computably enumerable degrees
MaRDI profile type: Publication
full work available at URL: s001530100111
OpenAlex ID: W2014247151
DOI: 10.1007/S001530100111
description: scientific article; zbMATH DE number 1982474