An Algebraic Approach to Filtrations for Superintuitionistic Logics

There are two standard model-theoretic methods for proving the finite model property for modal and superintuionistic logics, the standard filtration and the selective filtration. While the corresponding algebraic descriptions are better understood in modal logic, it is our aim to give similar algebraic descriptions of filtrations for superintuitionistic logics via locally finite reducts of Heyting algebras. We show that the algebraic description of the standard filtration is based on the →-free reduct of Heyting algebras, while that of selective filtration on the ∨-free reduct.