Reclassifying the antithesis of Specker's theorem
type: Item
instance of: scholarly article
title: Reclassifying the antithesis of Specker's theorem
zbMATH Open document ID: 1264.03125
author: Hannes Diener
published in: Archive for Mathematical Logic
publication date: 2013-02-04T00:00:00Z
review text: In this paper, instances of the anti-Specker property are classified in the fashion of constructive reverse mathematics. The anti-Specker property is a semi-constructive compactness principle. A subspace \(X\) of a metric space \(Y\) has the anti-Specker (\(\mathsf{AS}^Y_X\)) property, if any sequence in \(Y\) that is eventually bounded away from any point in \(X\), is eventually bounded away from the entire set \(X\). The main result of this paper is that \(\mathsf{AS}^{\mathbb{R}^2}_{[0,1]}\), \(\mathsf{AS}^Y_X\) for any compact subspace \(X\) of \(Y\), and the fan theorem for \(\Pi^0_1\)-bars are equivalent. This result should be compared with [\textit{D. Bridges} and \textit{H. Diener}, Math. Log. Q. 56, No.~4, 434--441 (2010; Zbl 1206.03053)] where it was shown that \(\mathsf{AS}^{\mathbb{R}}_{[0,1]}\) is equivalent to the fan theorem for so-called \(c\)-bars.
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 03B30
Mathematics Subject Classification ID: 03F65
zbMATH DE Number: 6134289
zbMATH Keywords: Specker sequence
zbMATH Keywords: anti-Specker property
zbMATH Keywords: Brouwer's fan theorem
zbMATH Keywords: constructive reverse mathematics
zbMATH Keywords: constructive mathematics
reviewed by: Alexander P. Kreuzer
MaRDI profile type: Publication
full work available at URL: s00153-012-0292-9
OpenAlex ID: W2055084678
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Wikidata QID: Q127416686
DOI: 10.1007/S00153-012-0292-9
description: scientific article; zbMATH DE number 6134289