Interpolation properties of superintuitionistic logics

Studia Logica 38 (4):419 - 428 (1979)
A family of prepositional logics is considered to be intermediate between the intuitionistic and classical ones. The generalized interpolation property is defined and proved is the following.Theorem on interpolation. For every intermediate logic L the following statements are equivalent:(i) Craig's interpolation theorem holds in L, (ii) L possesses the generalized interpolation property, (iii) Robinson's consistency statement is true in L.
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William Craig (1957). [Omnibus Review]. Journal of Symbolic Logic 22 (4):360-363.
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