TL;DR
This paper reviews Brouwer's fan theorem within Bishop's constructive mathematics, exploring its connections to the weak K"onig lemma and the uniform continuity theorem, and discussing its status as an axiom.
Contribution
It provides an overview of the status and relationships of Brouwer's fan theorem in constructive mathematics, highlighting its foundational significance.
Findings
The fan theorem is equivalent to the weak K"onig lemma in certain contexts.
The fan theorem implies the uniform continuity theorem.
The paper clarifies the role of the fan theorem as an axiom in constructive mathematics.
Abstract
Brouwer's fan theorem states that every bar is a uniform bar. We give an overview of the status of this axiom in Bishop's constructive mathematics. In particular, we describe the relationship between the fan theorem, the weak K\"onig lemma, and the uniform continuity theorem.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Topology and Set Theory · Advanced Algebra and Logic