Failure of interpolation in relevant logics (Q689074)

By a sophisticated geometrical construction (using the fact that a non- Arguesian projective plane cannot be imbedded into a three-dimensional projective space), it is shown that Craig's interpolation theorem fails for entailment \(E\), relevant logic \(R\), for the logic \(T\) of ticket entailment and for a large class of related systems. It is indicated how to use these results to show failure of the amalgamation property in many varieties of distributive lattice-ordered monoids.