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.
@article{1183742161,
author = {Seldin, Jonathan P.},
title = {On the Proof Theory of the Intermediate Logic MH},
journal = {J. Symbolic Logic},
volume = {51},
number = {1},
year = {1986},
pages = { 626-647},
language = {en},
url = {http://dml.mathdoc.fr/item/1183742161}
}
Seldin, Jonathan P. On the Proof Theory of the Intermediate Logic MH. J. Symbolic Logic, Tome 51 (1986) no. 1, pp. 626-647. http://gdmltest.u-ga.fr/item/1183742161/