| Abstract: | Predicate superintuitionistic logics are considered. We prove that all such logics that contain a logic characterized by frames
whose domains are all finite and are contained in the classical logic of finite domains do not have the interpolation and
Beth properties. It is also established that the interpolation property is not shared by all predicate superintuitionistic
logics which contain a logic characterized by frames whose domains of nonfinal worlds are all finite and which are contained
in a logic characterized by all two-element frames with finite constant domains.
Supported by the Competitive Basic Research Center of St. Petersburg State University, grant No. 93-1-88-12.
Translated fromAlgebra i Logika, Vol. 35, No. 1, pp. 105–117, January–February, 1996. |
