On the proof theory of the intermediate logic MH1

Publisher: Cambridge University Press

E-ISSN: 1943-5886|51|3|626-647

ISSN: 0022-4812

Source: The Journal of Symbolic Logic, Vol.51, Iss.3, 1986-09, pp. : 626-647

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Abstract

A natural deduction formulation is given for the intermediate logic called MH by Gabbay in [4]. Proof-theoretic methods are used to show that every deduction can be normalized, that MH is the weakest intermediate logic for which the Glivenko theorem holds, and that the Craig-Lyndon interpolation theorem holds for it.