A canonical topological model for extensions of K4 (Q969431)

In the absence of the axiom \(A\to\lozenge A\), formula \(\lozenge A\) can be interpreted as the derived set of \(A\), that is, the set of limit points of \(A\) in topological semantics. The author gives sufficient conditions for the completeness of (what he calls) a canonical topological model for extensions of K4. Systems K4, \(\text{K}4+\lozenge T\), K45 and several others are complete in this sense, while K4B and \(\text{K}4+\lozenge\phi\to\square \phi\) are not.