The double negation of the intermediate value theorem
type: Item
instance of: scholarly article
title: The double negation of the intermediate value theorem
zbMATH Open document ID: 1233.03060
author: Mohammad Ardeshir
author: Rasoul Ramezanian
published in: Annals of Pure and Applied Logic
publication date: 2011-08-26T00:00:00Z
review text: This paper studies the double negation of the intermediate value theorem for monotonous, continuous functions in an intuitionistic (constructive) setting. It is proved that if there exists a monotonous, continuous function for which the double negation of the intermediate value property doesn't hold, then there exists a Specker sequence. Furthermore, under the same assumption, there also exists an intuitionistically enumerable subset that is not decidable. A further main result of the paper is that there exists a monotonous, continuous function for which the double negation of the intermediate value property doesn't hold if and only if there exists a strong Specker double sequence. The authors relate their results to the open question of whether there exists a continuous function (so: not necessarily monotonous) for which the double negation of the intermediate value property doesn't hold. Two related articles are [\textit{M. Ardeshir} and \textit{R. Ramezanian}, Math. Log. Q. 55, No. 6, 637--648 (2009; Zbl 1192.03046)] and [\textit{W. Veldman}, J. UCS 11, No. 12, 2142--2158 (2005; Zbl 1128.03049)].
reviewed by: Iris Loeb
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 03F60
zbMATH DE Number: 5943616
zbMATH Keywords: decidability
zbMATH Keywords: intuitionistic mathematics
zbMATH Keywords: intermediate value theorem
zbMATH Keywords: Specker sequence
MaRDI profile type: Publication
full work available at URL: j.apal.2009.06.005
OpenAlex ID: W1978060594
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DOI: 10.1016/J.APAL.2009.06.005
description: scientific article; zbMATH DE number 5943616