Equivalents of the (weak) fan theorem

Annals of Pure and Applied Logic 132 (1):51-66 (2005)
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Abstract

This article presents a weak system of intuitionistic second-order arithmetic, WKV, a subsystem of the one in S.C. Kleene, R.E. Vesley [The Foundations of Intuitionistic Mathematics: Especially in Relation to Recursive Functions, North-Holland Publishing Company, Amsterdam, 1965]. It is then shown that some statements of real analysis, like a version of the Heine–Borel Theorem, and some statements of logic, e.g. compactness of classical proposition calculus, are equivalent to the Fan Theorem in this system

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Iris Loeb
VU University Amsterdam

References found in this work

Heine-borel does not imply the Fan theorem.Ieke Moerdijk - 1984 - Journal of Symbolic Logic 49 (2):514-519.

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