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

Josef Berger; Hajime Ishihara; Peter Schuster

Titles

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, Number 47, pp. 63 - 86

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

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

Josef Berger

Ludwig-Maximilians-Universität München

Hajime Ishihara

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

Peter Schuster

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%

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English

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Number of downloads: 1924

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