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The Weak Kőnig Lemma, Brouwer’s Fan Theorem, De Morgan’s Law, and Dependent Choice

Publication date: 23.08.2012

Reports on Mathematical Logic, 2012, Number 47, pp. 63 - 86

https://doi.org/10.4467/20842589RM.12.003.0684

Authors

,
Josef Berger
Ludwig-Maximilians-Universität München
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,
Hajime Ishihara
Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan
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Peter Schuster
Dipartimento di Informatica, Università degli Studi di Verona Strada le Grazie 15, 37134 Verona, Italy
Leeds University
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Titles

The Weak Kőnig Lemma, Brouwer’s Fan Theorem, De Morgan’s Law, and Dependent Choice

Abstract

The standard omniscience principles are interpreted in a systematic way within the context of binary trees. With this dictionary at hand we revisit the weak Konig lemma (WKL) and Brouwer’s fan theorem (FAN). We first study how one can arrive from FAN at WKL, and then give a direct decomposition, without coding, of WKL into the lesser limited principle of omniscience and an instance of the principle of dependent choices. As a complement we provide, among other equivalents of the standard omniscience principles, a uniform method to formulate most of them.

References

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Information

Information: Reports on Mathematical Logic, 2012, pp. 63 - 86

Article type: Original article

Titles:

Polish:

The Weak Kőnig Lemma, Brouwer’s Fan Theorem, De Morgan’s Law, and Dependent Choice

English:

The Weak Kőnig Lemma, Brouwer’s Fan Theorem, De Morgan’s Law, and Dependent Choice

Authors

Ludwig-Maximilians-Universität München

Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

Dipartimento di Informatica, Università degli Studi di Verona Strada le Grazie 15, 37134 Verona, Italy

Leeds University

Published at: 23.08.2012

Article status: Open

Licence: None

Percentage share of authors:

Josef Berger (Author) - 33%
Hajime Ishihara (Author) - 33%
Peter Schuster (Author) - 34%

Article corrections:

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Publication languages:

English

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