The interpolation theorem in fragments of logics

In the first part of this paper, we prove that there are continuously many fragments of intuitionistic propositional calculus (IpC) which fail to have the interpolation property, thereby extending an earlier result. Our proof makes use of the Rieger-Nishimura lattice. The second part is devoted to transferring this result to fragments of classical predicate calculus (CPC): this is done by giving a translation T of fragments of IpC in fragments of CPC which preserves the interpolation property.