Fernández-Duque, David A sound and complete axiomatization for dynamic topological logic. (English) Zbl 1256.03025 J. Symb. Log. 77, No. 3, 947-969 (2012). Author’s abstract: Dynamic topological logic (\(\mathcal D \mathcal J \mathcal I\)) is a multimodal system for reasoning about dynamical systems. It is defined semantically and, as such, most of the work done in the field has been model-theoretic. In particular, the problem of finding a complete axiomatization for the full language of \(\mathcal D \mathcal J \mathcal I\) over the class of all dynamical systems has proven to be quite elusive.Here we propose to enrich the language to include a polyadic topological modality, originally introduced by Dawar and Otto in a different context. We then provide a sound axiomatization for \(\mathcal D \mathcal J \mathcal I\) over this extended language, and prove that it is complete. The polyadic modality is used in an essential way in our proof. 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