Subspaces of \(\mathbb{Q}\) whose d-logics do not have the FMP (Q453191)

Giving meaning to modal formulas in topological spaces, the \(\lozenge\)-operator is usually interpreted by taking the closure. But there is another prominent interpretation, viz by taking the derivate. This leads to the so-called \textit{d-semantics} of topological modal logic. In the paper under review, the authors continue their previous work on d-logics by proving that there are uncountably many ones arising from subspaces of \(\mathbb{Q}\) but not satisfying the finite model property.