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

DOI10.1016/J.APAL.2008.09.018zbMath1156.03056OpenAlexW1979207178MaRDI QIDQ1001912

Hannes Diener, Iris Loeb

Publication date: 19 February 2009

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2008.09.018

zbMATH Keywords

equicontinuityconstructive reverse mathematicsfan theoremuniform continuity theorem

Mathematics Subject Classification ID

Constructive and recursive analysis (03F60) Foundations of classical theories (including reverse mathematics) (03B30) Constructive real analysis (26E40) Intuitionistic mathematics (03F55)

Related Items (16)

On the constructive notion of closure maps ⋮ Constructive notions of equicontinuity ⋮ A MARRIAGE OF BROUWER’S INTUITIONISM AND HILBERT’S FINITISM I: ARITHMETIC ⋮ SEPARATING THE FAN THEOREM AND ITS WEAKENINGS ⋮ Realizability Models Separating Various Fan Theorems ⋮ Decidable fan theorem and uniform continuity theorem with continuous moduli ⋮ Factoring Out Intuitionistic Theorems: Continuity Principles and the Uniform Continuity Theorem ⋮ Some axioms for constructive analysis ⋮ Characterising Brouwer's continuity by bar recursion on moduli of continuity ⋮ A continuity principle equivalent to the monotone \(\Pi^0_1\) fan theorem ⋮ Toward a clarity of the extreme value theorem ⋮ From Bolzano‐Weierstraß to Arzelà‐Ascoli ⋮ Kronecker's density theorem and irrational numbers in constructive reverse mathematics ⋮ Glueing continuous functions constructively ⋮ SEPARATING THE FAN THEOREM AND ITS WEAKENINGS II ⋮ Bishop-Style Constructive Reverse Mathematics

Cites Work

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• Glueing continuous functions constructively
• A fan-theoretic equivalent of the antithesis of Specker's theorem
• Compactness under constructive scrutiny
• Unique solutions
• A Bizarre Property Equivalent to the -Fan Theorem
• Limited Omniscience and the Bolzano-Weierstrass Principle
• Elements of Intuitionistic Analysis. Rolle's Theorem and Complete, Totally bounded, Metric Spaces
• Elements of Intuitionistic Analysis II the Stone‐Weierstrass Theorem and Ascoli's Theorem
• Foundations of Real and Abstract Analysis
• The pseudocompactness of [0.1 is equivalent to the uniform continuity theorem]
• New Computational Paradigms
• Logical Approaches to Computational Barriers

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