Archive for Mathematical Logic 48 (5):437-448 (2009)
Abstract |
In the informal setting of Bishop-style constructive reverse mathematics we discuss the connection between the antithesis of Specker’s theorem, Ishihara’s principle BD-N, and various types of equicontinuity. In particular, we prove that the implication from pointwise equicontinuity to uniform sequential equicontinuity is equivalent to the antithesis of Specker’s theorem; and that, for a family of functions on a separable metric space, the implication from uniform sequential equicontinuity to uniform equicontinuity is equivalent to BD-N
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Keywords | Constructive Reverse mathematics Anti-specker property Pseudobounded Fan theorem |
Categories | (categorize this paper) |
DOI | 10.1007/s00153-009-0131-9 |
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References found in this work BETA
Nicht Konstruktiv Beweisbare Sätze der Analysis.Ernst Specker - 1949 - Journal of Symbolic Logic 14 (3):145-158.
Equivalents of the (Weak) Fan Theorem.Iris Loeb - 2005 - Annals of Pure and Applied Logic 132 (1):51-66.
Sequences of Real Functions on [0, 1] in Constructive Reverse Mathematics.Hannes Diener & Iris Loeb - 2009 - Annals of Pure and Applied Logic 157 (1):50-61.
Continuity Properties in Constructive Mathematics.Hajime Ishihara - 1992 - Journal of Symbolic Logic 57 (2):557-565.
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Citations of this work BETA
The Bolzano–Weierstrass Theorem is the Jump of Weak Kőnig’s Lemma.Vasco Brattka, Guido Gherardi & Alberto Marcone - 2012 - Annals of Pure and Applied Logic 163 (6):623-655.
The Anti-Specker Property, Positivity, and Total Boundedness.Douglas Bridges & Hannes Diener - 2010 - Mathematical Logic Quarterly 56 (4):434-441.
On the Failure of BD-ࡃ and BD, and an Application to the Anti-Specker Property.Robert S. Lubarsky - 2013 - Journal of Symbolic Logic 78 (1):39-56.
On the Constructive Notion of Closure Maps.Mohammad Ardeshir & Rasoul Ramezanian - 2012 - Mathematical Logic Quarterly 58 (4-5):348-355.
Uniform Continuity Properties of Preference Relations.Douglas S. Bridges - 2008 - Notre Dame Journal of Formal Logic 49 (1):97-106.
View all 6 citations / Add more citations
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