Coding of real‐valued continuous functions under WKL$\mathsf {WKL}$.
Published In: Mathematical Logic Quarterly, 2023, v. 69, n. 3. P. 370 1 of 3
Database: Academic Search Ultimate 2 of 3
Authored By: Kawai, Tatsuji 3 of 3
Abstract
In the context of constructive reverse mathematics, we show that weak Kőnig's lemma (WKL$\mathsf {WKL}$) implies that every pointwise continuous function f:[0,1]→R$f : [0,1]\rightarrow \mathbb {R}$ is induced by a code in the sense of reverse mathematics. This, combined with the fact that WKL$\mathsf {WKL}$ implies the Fan theorem, shows that WKL$\mathsf {WKL}$ implies the uniform continuity theorem: every pointwise continuous function f:[0,1]→R$f : [0,1]\rightarrow \mathbb {R}$ has a modulus of uniform continuity. Our results are obtained in Heyting arithmetic in all finite types with quantifier‐free axiom of choice. [ABSTRACT FROM AUTHOR]
Additional Information
- Source:Mathematical Logic Quarterly. 2023/08, Vol. 69, Issue 3, p370
- Document Type:Article
- Subject Area:Mathematics
- Publication Date:2023
- ISSN:0942-5616
- DOI:10.1002/malq.202200031
- Accession Number:170748958
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