Game semantics of Martin-Löf type theory, part III: its consistency with Church's thesis
@article{Yamada2020GameSO,
title={Game semantics of Martin-L{\"o}f type theory, part III: its consistency with Church's thesis},
author={Norihiro Yamada},
journal={ArXiv},
year={2020},
volume={abs/2007.08094}
}We prove consistency of intensional Martin-Lof type theory (MLTT) with formal Church's thesis (CT), which was open for at least fifteen years. The difficulty in proving the consistency is that a standard method of realizability a la Kleene does not work for the consistency, though it validates CT, as it does not model MLTT; specifically, the realizability does not validate MLTT's congruence rule on pi-types (known as the $\xi$-rule). We overcome this point and prove the consistency by novel…
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