Abstract : In this paper we study the expressive power and definability for (extended) modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt-thomason definability theorem in terms of the well-established first-order topological language Lt.
Balder ten Cate, Gabelaia David, Dmitry Sustretov. Modal languages for topology: Expressivity and definability. Annals of Pure and Applied Logic, Elsevier Masson, 2009, 159 (1-2), pp.146-170. ⟨10.1016/j.apal.2008.11.001⟩. ⟨inria-00424693⟩