 Lemmon (1966a and 1966b) adapts the algebraic methods of McKinsey to prove decidability results and representation theorems for various modal systems including T (though apparently in ignorance of Jónsson and Tarski’s work). In particular, he extends McKinsey’s method by introducing a new technique for constructing finite algebras of subsets of a Kripke model structure (discussed in the next section of this entry). Lemmon (1966b: 191) attributes to Dana Scott the main result of his second 1966 paper. This is a general representation theorem proving that algebras for modal systems can be represented as algebras based on the power set of the set K in the corresponding Kripke’s structures. As a consequence, algebraic completeness translates into Kripke’s model theoretic completeness. So, Lemmon elucidates very clearly the connection between Kripke’s models whose elements are worlds and the corresponding algebras whose elements are sets of worlds that can be thought of as propositions, thereby showing that the algebraic and model theoretic results are deeply connected. Kripke (1963a) is already explicit on this connection. In The Lemmon Notes (1977), written in collaboration with Dana Scott and edited by Segerberg, the 1966 technique is transformed into a purely model theoretic method which yields completeness and decidability results for many systems of modal logic in as general a form as possible (1977: 29).