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The weak König lemma and uniform continuity

  • Josef Berger (a1)
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.

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[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.
[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.
[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.
[4]Troelstra, Anne S., Metamathematical Investigation of Intuitionistic Arithmetic and Aalysis, Lecture Notes in Mathematics, vol. 344, Springer-Verlag, 1973.
[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.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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