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Lubarsky, Robert S.
2022.
Revolutions and Revelations in Computability.
Vol. 13359,
Issue. ,
p.
162.
Published online by Cambridge University Press: 25 July 2019
Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Earlier work showed all of these implications to be strict. Here we reprove one of the strictness results, using very different arguments. The technique used is a mixture of realizability, forcing in the guise of Heyting-valued models, and Kripke models.