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

Notre Dame Journal of Formal Logic 47 (2):249-252 (2006)
  Copy   BIBTEX

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

Categories

Keywords

Reprint years

DOI

10.1305/ndjfl/1153858649

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 107,286

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

König's lemma, weak König's lemma, and the decidable fan theorem.Makoto Fujiwara - 2021 - Mathematical Logic Quarterly 67 (2):241-257.
Classifying Dini's Theorem.Josef Berger & Peter Schuster - 2006 - Notre Dame Journal of Formal Logic 47 (2):253-262.
Brouwer's fan theorem and unique existence in constructive analysis.Josef Berger & Hajime Ishihara - 2005 - Mathematical Logic Quarterly 51 (4):360-364.
A Weak Constructive Sequential Compactness Property And The Fan Theorem.Douglas Bridges - 2005 - Logic Journal of the IGPL 13 (2):151-158.
Aligning the weak König lemma, the uniform continuity theorem, and Brouwer’s fan theorem.Josef Berger - 2012 - Annals of Pure and Applied Logic 163 (8):981-985.
The Weak Koenig Lemma, Brouwer's Fan Theorem, De Morgan's Law, and Dependent Choice.Josef Berger, Hajime Ishihara & Peter Schuster - 2012 - Reports on Mathematical Logic:63-86.
Reclassifying the antithesis of Specker’s theorem.Hannes Diener - 2012 - Archive for Mathematical Logic 51 (7-8):687-693.
On Some of Brouwer’s Axioms.Wim Veldman - 2025 - Bulletin of Symbolic Logic 31 (1):1-52.
Coding of real‐valued continuous functions under WKL$\mathsf {WKL}$.Tatsuji Kawai - 2023 - Mathematical Logic Quarterly 69 (3):370-391.
Reverse mathematics and a Ramsey-type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.

Analytics

Added to PP
2010-08-24

Downloads
82 (#283,262)

6 months
13 (#312,861)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Unique solutions.Peter Schuster - 2006 - Mathematical Logic Quarterly 52 (6):534-539.

View all 11 citations / Add more citations

References found in this work

Formal systems for some branches of intuitionistic analysis.G. Kreisel - 1970 - Annals of Mathematical Logic 1 (3):229.
Note on the Fan theorem.A. S. Troelstra - 1974 - Journal of Symbolic Logic 39 (3):584-596.
An omniscience principle, the König Lemma and the Hahn-Banach theorem.Hajime Ishihara - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (3):237-240.

Add more references