Finite condensations of recursive linear orders
type: Item
instance of: scholarly article
title: Finite condensations of recursive linear orders
zbMATH Open document ID: 0673.03034
DOI: 10.1007/BF00671562
author: Dev K. Roy
author: Richard Watnick
published in: Studia Logica
publication date: 1988-01-01T00:00:00Z
review text: This paper answers a question raised by J. Rosenstein: that of locating, in the arithmetical hierarchy, the finite condensation of a recursive linear order type. It was proved that (1) there is a recursive linear order whose finite condensation has \(\Pi_ 2-\Pi_ 1\) order type, (2) a linear order type is \(\Pi_{2n}\) iff it is the n-fold finite condensation of a recursive type, and (3) for all \(n\geq 2\) an order type is \(\Pi_ n\) iff it is \(\Sigma_ n\) presented.
reviewed by: Li Xiang
Mathematics Subject Classification ID: 03D55
Mathematics Subject Classification ID: 06A05
zbMATH DE Number: 4101165
zbMATH Keywords: arithmetical hierarchy
zbMATH Keywords: finite condensation of a recursive linear order type
MaRDI profile type: Publication
cites work: R. e. presented linear orders
cites work: Linear Order Types of Nonrecursive Presentability
cites work: A generalization of Tennenbaum's theorem on effectively finite recursive linear orderings
full work available at URL: https://doi.org/10.1007/bf00671562
OpenAlex ID: W2074465079
description: scientific article; zbMATH DE number 4101165