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The reverse mathematics of the Tietze extension theorem


Author: Paul Shafer
Journal: Proc. Amer. Math. Soc. 144 (2016), 5359-5370
MSC (2010): Primary 03B30, 03F35, 03F60
DOI: https://doi.org/10.1090/proc/13217
Published electronically: June 10, 2016
MathSciNet review: 3556278
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Abstract: We prove that several versions of the Tietze extension theorem for functions with moduli of uniform continuity are equivalent to $ \mathsf {WKL}_0$ over $ \mathsf {RCA}_0$. This confirms a conjecture of Giusto and Simpson (2000) that was also phrased as a question in Montalbán's Open questions in reverse mathematics (2011).


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Additional Information

Paul Shafer
Affiliation: Department of Mathematics, Ghent University, Krijgslaan 281 S22, B-9000 Ghent, Belgium
Email: paul.shafer@ugent.be

DOI: https://doi.org/10.1090/proc/13217
Keywords: Computability theory, reverse mathematics, Tietze extension theorem
Received by editor(s): February 17, 2016
Published electronically: June 10, 2016
Additional Notes: The author is an FWO Pegasus Long Postdoctoral Fellow.
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2016 American Mathematical Society