Extracting information from intermediate T-systems

In this paper we will study the problem of uniformly extracting information from constructive and semiconstructive calculi. We will define an information extraction mechanism and will explain several examples of systems to which such a mechanism can be applied. In particular, we will give as examples some families of effective subsystems of a wide class of very large intermediate theories, we call T-systems. These large T-systems, even if ineffective and semantically defined, provide a uniform and fruitful framework where to analyze the possible combinations in a uniformly constructive context of mathematical and super-intuitionistic logical principles.

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