نبذة مختصرة : International audience ; Introduction : Iterated structures are bi-relational Kripke frames where each relation is a strict partial order and additionally second relation is the greatest fixed point of the first relation under monotone operator on the lattice of all partial orders included in the first relation. The study of these structures closely relates to the modal logic study of Cantor Bendixon rank. The details about this connection as well as important results around this study could be found in [2] In this work we touch the issue of modal definability of iterated strict partial orders. The modal logic of iterated strict partial orders is studied in [2] where we present the complete axiomatisation of the logic. The logic is axiomatised by the following modal formulas 2φ →22φ, 2?φ → 2?2?φ, 2φ → 2?φ, 2?φ → 22?φ, 2?φ → 2?2φ, 22?φ → 2?φ. Moreover we prove that the class of iterated structures is not first order definable and that the modality 2∗ interpreted on the second relation is not modally definable. In this paper we prove that the class of iterated structures is not modally definable either.
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