On Church's Thesis in Cubical Assemblies

05/08/2019

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by   Andrew Swan, et al.

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We show that Church's thesis, the axiom stating that all functions on the naturals are computable, does not hold in the cubical assemblies model of cubical type theory. We show that nevertheless Church's thesis is consistent with univalent type theory by constructing a reflective subuniverse of cubical assemblies where it holds.