The anti-Specker property, a Heine-Borel property, and uniform continuity
type: Item
instance of: scholarly article
title: The anti-Specker property, a Heine-Borel property, and uniform continuity
zbMATH Open document ID: 1143.03031
author: Josef Berger
author: Douglas Bridges
published in: Archive for Mathematical Logic
publication date: 2008-05-26T00:00:00Z
review text: The paper contributes to the ongoing program of constructive reverse mathematics. It investigates a very weak version of the Heine-Borel property for subsets of the real line. It is shown that this property is satisfied whenever the space satisfies a strong antithesis of the existence of a Specker sequence (that is, a bounded sequence of real numbers that does not converge). The latter property can be seen as an intuitionistic version of sequential compactness. Furthermore reasons are given why the converse does not hold. The paper then continues and investigates the relations between the two above-mentioned principles and the uniform continuity principle for integer-valued functions. The paper is of relevance to anybody interested in (constructive) reverse mathematics, recursive/constructive analysis and foundational issues related to the continuum.
reviewed by: Hannes Diener
Mathematics Subject Classification ID: 03F65
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 03B30
zbMATH DE Number: 5278972
zbMATH Keywords: constructive reverse mathematics
zbMATH Keywords: sequential compactness
zbMATH Keywords: Specker sequence
MaRDI profile type: Publication
full work available at URL: s00153-007-0063-1
OpenAlex ID: W1976398594
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DOI: 10.1007/S00153-007-0063-1
description: scientific article; zbMATH DE number 5278972