Separating the Fan theorem and its weakenings

Journal of Symbolic Logic 79 (3):792-813 (2014)

Abstract
Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.
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DOI 10.1017/jsl.2014.9
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Independence Results Around Constructive ZF.Robert S. Lubarsky - 2005 - Annals of Pure and Applied Logic 132 (2-3):209-225.

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