 Of great importance is the paper “Semantical Analysis of Modal Logic I” (Kripke 1963a) where normal systems are treated. It is here that Kripke fully develops the analogy with the algebraic results of Jónsson and Tarski and proves completeness and decidability for propositional systems T, S4, S5, and B (the Brouwersche system), which is here introduced. Kripke claims to have derived on his own the main theorem of “Boolean Algebras with Operators” by an algebraic analog of his own semantical methods (69, fn. 2). It is in this paper that the two additional crucial generalizations of the model theory are introduced. The first is the new understanding of the elements \(H\) of \(K\) as simple indices, not assignments of values. Once this change is introduced, the models have to be supplemented by an auxiliary function \(\Phi\) needed to assign values to the propositional variables relative to worlds. Hence, while in the 1959 model theory 