 In 1963a Kripke “asks various questions concerning the relation \(R\)” (1963a: 70). First, he shows that every satisfiable formula has a connected model, i.e., a model based on a model structure \((G, K, R)\) where for all \(H\in K\), \(G\mathrel{R*}H\), where \(R*\) is the ancestral relation corresponding to \(R\). Hence, only connected models need to be considered. Then, Kripke shows the nowadays well-known results that axiom 4 corresponds to the transitivity of the relation \(R\), that axiom \(B\) correspond to symmetry, and that the characteristic axiom of S5 added to system T corresponds to \(R\) being an equivalence relation. Using the method of tableaux, completeness for the modal propositional systems T, S4, S5, and B vis-à-vis the appropriate class of models (reflexive structures for T) is proved. The decidability of these systems, including the more complex case of S4, is also proved. (For a more detailed treatment of frames, consult the SEP entry on  modal logic.)