The reverse mathematics of the Tietze extension theorem
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- by Paul Shafer
- Proc. Amer. Math. Soc. 144 (2016), 5359-5370
- DOI: https://doi.org/10.1090/proc/13217
- Published electronically: June 10, 2016
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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).References
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Bibliographic Information
- Paul Shafer
- Affiliation: Department of Mathematics, Ghent University, Krijgslaan 281 S22, B-9000 Ghent, Belgium
- MR Author ID: 920651
- ORCID: 0000-0001-5386-9218
- Email: paul.shafer@ugent.be
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 5359-5370
- MSC (2010): Primary 03B30, 03F35, 03F60
- DOI: https://doi.org/10.1090/proc/13217
- MathSciNet review: 3556278