Notre Dame Journal of Formal Logic

Weak König's Lemma Implies Brouwer's Fan Theorem: A Direct Proof

Hajime Ishihara

Abstract

Classically, weak König's lemma and Brouwer's fan theorem for detachable bars are equivalent. We give a direct constructive proof that the former implies the latter.

Article information

Source
Notre Dame J. Formal Logic, Volume 47, Number 2 (2006), 249-252.

Dates
First available in Project Euclid: 25 July 2006

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1153858649

Digital Object Identifier
doi:10.1305/ndjfl/1153858649

Mathematical Reviews number (MathSciNet)
MR2240622

Zentralblatt MATH identifier
1111.03052

Subjects
Primary: 03F65: Other constructive mathematics [See also 03D45]
Secondary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35]

Keywords
weak Koenig's lemma Brouwer's fan theorem constructive mathematics

Citation

Ishihara, Hajime. Weak König's Lemma Implies Brouwer's Fan Theorem: A Direct Proof. Notre Dame J. Formal Logic 47 (2006), no. 2, 249--252. doi:10.1305/ndjfl/1153858649. https://projecteuclid.org/euclid.ndjfl/1153858649


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References

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  • [3] Troelstra, A. S., "Note on the fan theorem", The Journal of Symbolic Logic, vol. 39 (1974), pp. 584--96.
  • [4] Troelstra, A. S., and D. van Dalen, Constructivism in Mathematics. Vol. I, vol. 121 of Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam, 1988.