The Kierstead's conjecture and limitwise monotonic functions
type: Item
instance of: scholarly article
title: The Kierstead's conjecture and limitwise monotonic functions
zbMATH Open document ID: 1459.03066
author: Guohua Wu
author: M. V. Zubkov
published in: Annals of Pure and Applied Logic
publication date: 2018-04-06T00:00:00Z
review text: A linear order is \(\Pi_1^0\)-rigid if it does not have any nontrivial \(\Pi_1^0\)-automorphism. Let \(\zeta, \eta\) are the order types integers and rational numbers, respectively. \textit{H. A. Kierstead} [J. Symb. Log. 52, 681--688 (1987; Zbl 0637.03043)] conjectured that every computable copy of a linear order \(\mathcal L\) has a strongly nontrivial \(\Pi_1^0\)-automorphism if and only if \(\mathcal L\) contains an interval of order type \(\eta\). In the paper under review, the authors prove this conjecture for linear orders whose order types are \(\Sigma_{q\in Q}F(q)\), where \(F\) is an extended \(\emptyset'\)-limitwise monotonic function, i.e. \(F\) can take the value \(\zeta\).
reviewed by: M. M. Arslanov
Mathematics Subject Classification ID: 03D45
Mathematics Subject Classification ID: 03C57
zbMATH DE Number: 6856630
zbMATH Keywords: recursive linear order
zbMATH Keywords: automorphism
zbMATH Keywords: limitwise monotonic function
Wikidata QID: Q122924579
MaRDI profile type: Publication
full work available at URL: j.apal.2018.01.003
OpenAlex ID: W2783463375
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DOI: 10.1016/J.APAL.2018.01.003
description: scientific article; zbMATH DE number 6856630