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

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.

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