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
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

Unique Solutions.Peter Schuster - 2006 - Mathematical Logic Quarterly 52 (6):534-539.
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.
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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