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The weak König lemma and uniform continuity

Published online by Cambridge University Press:  12 March 2014

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

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2008

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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. 249252.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. 92116.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