Rogers semilattices of families of two embedded sets in the Ershov hierarchy
type: Item
instance of: scholarly article
title: Rogers semilattices of families of two embedded sets in the Ershov hierarchy
zbMATH Open document ID: 1257.03071
author: Serikzhan A. Badaev
author: Andrea Sorbi
author: Mustafa Manat
publication date: 2012-09-12T00:00:00Z
full work available at URL: http://nur.nu.edu.kz/handle/123456789/972
Mathematics Subject Classification ID: 03D45
Mathematics Subject Classification ID: 03D55
zbMATH DE Number: 6081356
zbMATH Keywords: computable numbering
zbMATH Keywords: computable ordinal
zbMATH Keywords: ordinal notation
zbMATH Keywords: Ershov hierarchy
zbMATH Keywords: Rogers semilattice
MaRDI profile type: Publication
OpenAlex ID: W1983032418
cites work: Computable structures and the hyperarithmetical hierarchy
cites work: Q5619076
cites work: Q5619077
cites work: Generalized computable numerations and nontrivial Rogers semilattices
DOI: 10.1002/MALQ.201100114
published in: Mathematical Logic Quarterly (MLQ)
review text: This paper examines computable numberings, specifically the Rogers semilattices induced by families of sets at different levels of the Ershov hierarchy -- see [\textit{S. A. Badaev} and \textit{Zh. T. Talasbaeva}, in: Mathematical logic in Asia. Proceedings of the 9th Asian logic conference, Novosibirsk, Russia, 2005. Hackensack, NJ: World Scientific. 17--30 (2006; Zbl 1123.03042)]. The authors focus on the possible cardinality of such a semilattice, in particular, conditions under which the semilattice is infinite and conditions under which it is a singleton.
reviewed by: Leon Harkleroad
description: scientific article; zbMATH DE number 6081356