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What is the computational power of the Calculus of Constructions?

My understanding of András' answer is that, while it gets the gist correct, his final conclusion is not quite right: The "standard" way to determine the strength of the function space in a ...
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There is no total language where all total computable $\mathbb{N} \to \mathbb{N}$ functions are definable. In a total language, an interpreter for the same language is not definable because if it were ...