Abstract
In my paper [1], with which I assume the reader is familiar, I defined an arithmetic theory of constructions ATC and gave an interpretation of intuitionistic arithmetic HA in ATC. I proved that, in a suitable sense, every formula provable in HA is also provable in ATC. I proved the converse of this result only for positive sentences. In the present paper I will prove in full generality that any formula of HA which is provable in ATC is already provable in HA. In a later paper I shall use this result to obtain new information about certain extensions of HA by addition of higher types.
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