Embedding of countable orders in Turing degrees
type: Item
instance of: scholarly article
title: Embedding of countable orders in Turing degrees
zbMATH Open document ID: 1025.03033
DOI: 10.1023/A:1021400820931
author: Sh. T. Ishmukhametov
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: Consider a descending sequence \(\{{\mathbf c}_i\)\} of nonzero Turing degrees in which the reductions \textbf{c}\(_{i+1}\leq{\mathbf c}_i\) can be carried out uniformly in \({\mathbf 0}'\). The author shows that, in fact, the reductions can be carried out uniformly and that there exists a nonzero degree below every \({\mathbf c}_i\). In particular, such a sequence cannot form an initial segment of nonzero degrees.
Mathematics Subject Classification ID: 03D28
Mathematics Subject Classification ID: 03D20
zbMATH DE Number: 1928328
zbMATH Keywords: recursive function
zbMATH Keywords: Turing degrees
zbMATH Keywords: embedding method
zbMATH Keywords: ordering
zbMATH Keywords: lattice
reviewed by: Leon Harkleroad
MaRDI profile type: Publication
full work available at URL: a:1021400820931
OpenAlex ID: W61235908
description: scientific article; zbMATH DE number 1928328