The Weak Konig Lemma, Brouwer’s Fan Theorem, De Morgan’s Law, and Dependent Choice Cover Image

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

Author(s): Hajime Ishihara, Josef Berger, Peter Schuster
Subject(s): Philosophy
Published by: Wydawnictwo Uniwersytetu Jagiellońskiego

Summary/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 K˝onig 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.

  • Issue Year: 2012
  • Issue No: 47
  • Page Range: 63-86
  • Page Count: 24
  • Language: English