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 suffices to separate all of the as yet identified fan theorems.
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Lubarsky, R.S., Diener, H. (2013). Separating the Fan Theorem and Its Weakenings. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2013. Lecture Notes in Computer Science, vol 7734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35722-0_20
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DOI: https://doi.org/10.1007/978-3-642-35722-0_20
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