Filtrations of generalized Veltman models

The filtration method is often used to prove the finite model property of modal logics. We adapt this technique to the generalized Veltman semantics for interpretability logics. In order to preserve the defining properties of generalized Veltman models, we use bisimulations to define adequate filtrations. We give an alternative proof of the finite model property of interpretability logic IL w.r.t. Veltman models, and we prove the finite model property of the systems ILM and ILM_0 w.r.t. generalized Veltman models.