SEPARATING THE FAN THEOREM AND ITS WEAKENINGS
Robert S. Lubarsky, Hannes Diener · Journal of Symbolic Logic · 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.