Brouwer's fan theorem and unique existence in constructive analysis

Mathematical Logic Quarterly 51 (4):360-364 (2005)

Abstract
Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. Furthermore, we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum
Keywords unique existence  Constructive reverse mathematics  Brouwer's fan theorem
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DOI 10.1002/malq.200410038
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References found in this work BETA

An Omniscience Principle, the König Lemma and the Hahn-Banach Theorem.Hajime Ishihara - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (3):237-240.

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Citations of this work BETA

Brouwer’s Fan Theorem and Convexity.Josef Berger & Gregor Svindland - 2018 - Journal of Symbolic Logic 83 (4):1363-1375.
Some Axioms for Constructive Analysis.Joan Rand Moschovakis & Garyfallia Vafeiadou - 2012 - Archive for Mathematical Logic 51 (5-6):443-459.
Convexity and Unique Minimum Points.Josef Berger & Gregor Svindland - 2019 - Archive for Mathematical Logic 58 (1-2):27-34.

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