On partitioning Kripke frames of finite height

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The paper proves finite model property and decidability for a family of modal logics. A binary relation R is called pretransitive, if R*=∪ᵢ≤ ₘ Rⁱ for some m≥ 0, where R* is the transitive reflexive closure of R. By the height of (W,R) we mean the height of the preorder (W,R*). Special partitionings (filtrations) are described for pretransitive frames of finite height, which implies finite model property and decidability of logics of these frames.