| Abstract: | It is proved that in superintuitionistic logics, the projective Beth property follows from the Craig interpolation property,
but the converse does not hold. A criterion is found which allows us to reduce the problem asking whether the projective Beth
property is valid in superintuitionistic logics to suitable properties of varieties of pseudoboolean algebras. It is shown
that the principle of variable separation follows from the projective Beth property. On the other hand, the interpolation
property in a logic L implies the projective Beth property in Δ(L).
Supported by RFFR grants No. 96-01-01552 and No. 99-01-00600.
Translated fromAlgebra i Logika, Vol. 38, No. 6, pp. 680–696, November–December, 1999. |
