Abstract
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 a result of J.I. Zucker. 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.
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