Sequences of real functions on [0, 1] in constructive reverse mathematics
Annals of Pure and Applied Logic 157 (1):50-61 (2009)
| Authors |
Iris Loeb
VU University Amsterdam
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| Abstract |
We give an overview of the role of equicontinuity of sequences of real-valued functions on [0,1] and related notions in classical mathematics, intuitionistic mathematics, Bishop’s constructive mathematics, and Russian recursive mathematics. We then study the logical strength of theorems concerning these notions within the programme of Constructive Reverse Mathematics. It appears that many of these theorems, like a version of Ascoli’s Lemma, are equivalent to fan-theoretic principles
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| DOI | 10.1016/j.apal.2008.09.018 |
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References found in this work BETA
The Pseudocompactness of [0.1] Is Equivalent to the Uniform Continuity Theorem.Douglas Bridges & Hannes Diener - 2007 - Journal of Symbolic Logic 72 (4):1379 - 1384.
Compactness Under Constructive Scrutiny.Hajime Ishihara & Peter Schuster - 2004 - Mathematical Logic Quarterly 50 (6):540-550.
A Bizarre Property Equivalent To The -Fan Theorem.Josef Berger & Douglas Bridges - 2006 - Logic Journal of the IGPL 14 (6):867-871.
Elements of Intuitionistic Analysis II the Stone-Weierstrass Theorem and Ascoli's Theorem.H. de Swart - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):501-508.
View all 9 references / Add more references
Citations of this work BETA
Constructive Notions of Equicontinuity.Douglas S. Bridges - 2009 - Archive for Mathematical Logic 48 (5):437-448.
Glueing Continuous Functions Constructively.Douglas S. Bridges & Iris Loeb - 2010 - Archive for Mathematical Logic 49 (5):603-616.
A Continuity Principle Equivalent to the Monotone $$Pi ^{0}_{1}$$ Fan Theorem.Tatsuji Kawai - 2019 - Archive for Mathematical Logic 58 (3-4):443-456.
On the Constructive Notion of Closure Maps.Mohammad Ardeshir & Rasoul Ramezanian - 2012 - Mathematical Logic Quarterly 58 (4-5):348-355.
From Bolzano-Weierstraß to Arzelà-Ascoli.Alexander P. Kreuzer - 2014 - Mathematical Logic Quarterly 60 (3):177-183.
View all 6 citations / Add more citations
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