Ershov hierarchy and the T-jump
type: Item
instance of: scholarly article
title: Ershov hierarchy and the T-jump
zbMATH Open document ID: 0673.03033
DOI: 10.1007/BF01978401
published in: Algebra and Logic
publication date: 1988-01-01T00:00:00Z
review text: Let \((O,<_ O)\) be the Kleene system of ordinal symbols, let \(\Sigma_ a^{-1}\), \(\Delta_ a^{-1}\) (a\(\in O)\) be the classes of the Ershov hierarchy [see \textit{Yu. L. Ershov}'s papers, Algebra Logika 7, No.4, 15- 47 (1968; Zbl 0216.009) and ibid. 9, No.1, 34-51 (1970; Zbl 0233.02017)], and let ' be the T-jump operator. The following main theorem is proved: 1) For any r.e. set A and any \(a\in O\) not being the least one, there exists a set \(R\in \Sigma_ a^{-1}\) such that \(R'\equiv_ TA'\) and R is not T-equivalent to any set of \(\Delta_ a^{-1}\). 2) For any r.e. set A and any limit ordinal \(a\in O\) there exists a set \(R\in \Delta_ a^{-1}\) such that \(R'\equiv_ TA'\) and R is not T-equivalent to any set of \(\cup_{b<_ Oa}\Sigma_ b^{-1}\).
Mathematics Subject Classification ID: 03D55
Mathematics Subject Classification ID: 03D30
zbMATH DE Number: 4101164
zbMATH Keywords: Kleene system of ordinal symbols
zbMATH Keywords: Ershov hierarchy
zbMATH Keywords: T-jump operator
zbMATH Keywords: limit ordinal
author: Victor Selivanov
MaRDI profile type: Publication
cites work: Q5619077
cites work: Ershov hierarchy
cites work: Q4723717
cites work: Pseudo-jump operators. II: Transfinite iterations, hierarchies and minimal covers
cites work: Q3919704
full work available at URL: https://doi.org/10.1007/bf01978401
OpenAlex ID: W2034822263
description: scientific article; zbMATH DE number 4101164