Hostname: page-component-7dd5485656-hw7sx Total loading time: 0 Render date: 2025-10-30T02:07:53.427Z Has data issue: false hasContentIssue false
  • English
  • Français

The weak König lemma and uniform continuity

Published online by Cambridge University Press:  12 March 2014

Josef Berger
Josef Berger*
Affiliation:
Japan Advanced Institute of Science and Technology, School of Information Science, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan, E-mail: jberger@jaist.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove constructively that the weak König lemma and quantifier-free number–number choice imply that every pointwise continuous function from Cantor space into Baire space has a modulus of uniform continuity.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 3 , September 2008 , pp. 933 - 939
Copyright
Copyright © Association for Symbolic Logic 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Berger, Josef, Weak König's lemma implies the Fan Theorem for c-bars, Computation and Logic in the Real World, CiE 2007, Quaderni del Dipartimento di Scienze Matematiche e Informatiche “Roberto Magari”, University of Siena, 2007.Google Scholar
[2]Ishihara, Hajime, Weak König's lemma implies Brouwer's Fan Theorem: A direct proof, Notre Dame Journal of Formal Logic, vol. 47 (2006), no. 2, pp. 249–252.CrossRefGoogle Scholar
[3]Kohlenbach, Ulrich, Foundational and mathematical uses of higher types, Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman (Sieg, W., Sommer, R., and Talcott, C., editors), Lecture Notes in Logic, vol. 15, A. K. Peters, 2002, pp. 92–116.Google Scholar
[4]Troelstra, Anne S., Metamathematical Investigation of Intuitionistic Arithmetic and Aalysis, Lecture Notes in Mathematics, vol. 344, Springer-Verlag, 1973.CrossRefGoogle Scholar
[5]Troelstra, Anne S. and van Dalen, Dirk, Constructivism in Mathematics. An Introduction. Vol. land II, Studies in Logic and the Foundation of Mathematics, vol. 121 and 123, North-Holland, 1988.Google Scholar