Weak König's Lemma Implies Brouwer's Fan Theorem: A Direct Proof
Hajime Ishihara
Source: Notre Dame J. Formal Logic Volume 47, Number 2
(2006), 249-252.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1153858649
Digital Object Identifier: doi:10.1305/ndjfl/1153858649
Mathematical Reviews number (MathSciNet): MR2240622
References
[1] Ishihara, H., "An omniscience principle, the König lemma and the Hahn-Banach theorem", Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 36 (1990), pp. 237--40.
Mathematical Reviews (MathSciNet): MR92m:03095
Zentralblatt MATH: 0684.03024
Digital Object Identifier: doi:10.1002/malq.19900360307
[2] Kreisel, G., and A. S. Troelstra, "Formal systems for some branches of intuitionistic analysis", Annals of Pure and Applied Logic, vol. 1 (1970), pp. 229--387.
Mathematical Reviews (MathSciNet): MR41:8210
Zentralblatt MATH: 0211.01101
[3] Troelstra, A. S., "Note on the fan theorem", The Journal of Symbolic Logic, vol. 39 (1974), pp. 584--96.
Mathematical Reviews (MathSciNet): MR52:5371
Zentralblatt MATH: 0306.02026
Digital Object Identifier: doi:10.2307/2272902
Project Euclid: euclid.jsl/1183739194
[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.
Mathematical Reviews (MathSciNet): MR90e:03002a
Zentralblatt MATH: 0653.03040
Notre Dame Journal of Formal Logic
