Sequences of real functions on [0, 1] in constructive reverse mathematics

Annals of Pure and Applied Logic 157 (1):50-61 (2009)
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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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Iris Loeb
VU University Amsterdam

Citations of this work

Constructive Mathematics.Douglas Bridges - 2008 - Stanford Encyclopedia of Philosophy.
Constructive Notions of Equicontinuity.Douglas S. Bridges - 2009 - Archive for Mathematical Logic 48 (5):437-448.
Separating the Fan Theorem and its Weakenings.Robert S. Lubarsky & Hannes Diener - 2014 - Journal of Symbolic Logic 79 (3):792-813.

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References found in this work

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.

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