The \(\Delta_2^0\)-spectrum of a linear order
type: Item
instance of: scholarly article
zbMATH Open document ID: 0992.03050
DOI: 10.2307/2695025
publication date: 2002-09-05T00:00:00Z
Mathematics Subject Classification ID: 03D25
zbMATH DE Number: 1658156
zbMATH Keywords: spectrum
zbMATH Keywords: linear order
zbMATH Keywords: structures
zbMATH Keywords: Turing degrees
author: Russell Miller
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2695025
OpenAlex ID: W1970404779
cites work: Enumerations, countable structures and Turing degrees
cites work: Relative to any nonrecursive set
cites work: Q3949052
cites work: Degrees coded in jumps of orderings
cites work: Computable homogeneous Boolean algebras
cites work: Degrees of orderings not isomorphic to recursive linear orderings
title: The \(\Delta_2^0\)-spectrum of a linear order
published in: The Journal of Symbolic Logic
review text: The spectrum \(\text{Spec}(S)\) of an algebraic structure \(S\) is the class of Turing degrees of presentations of \(S\). Slaman and independently Wehner constructed an example of a structure with \(\text{Spec}(S)= {\mathbf D}\setminus \{\mathbf{0}\}\) where \textbf{D} is the class of all Turing degrees. Answering a question of Downey, the author constructs an example of a linear order whose spectrum includes every non-computable \(\Delta_2^0\)-degree.
reviewed by: Sh. T. Ishmukhametov
description: scientific article; zbMATH DE number 1658156