A note on sequent calculi intermediate between LJ and LK

Studia Logica 47 (2):151 - 157 (1988)
Abstract
We prove that every finitely axiomatizable extension of Heyting's intuitionistic logic has a corresponding cut-free Gentzen-type formulation. It is shown how one can use this result to find the corresponding normalizable natural deduction system and to give a criterion for separability of considered logic. Obviously, the question how to obtain an effective definition of a sequent calculus which corresponds to a concrete logic remains a separate problem for every logic.
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Gaisi Takeuti (1987). Proof Theory. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
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