Weak König’s Lemma Implies the Uniform Continuity Theorem

Article type: Research Article

Authors: Diener, Hannes^;

Affiliations: University of Siegen, Germany, [email protected]

Note: [] This research was supported by a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme.

Abstract: As the title suggests we are going to show that Weak König’s Lemma implies the uniform continuity theorem; to be more precise the uniform continuity theorem for functions $[0,1] \to \R$. This improves upon a result by J. Berger who has proven this implication for functions $[0,1] \to \N$.

Keywords: Weak König Lemma, uniform continuity theorem, reverse mathematics

DOI: 10.3233/COM-13009

Journal: Computability, vol. 2, no. 1, pp. 9-13, 2013