Abstract

McKinsey Axiom is the modal formula LMA $\to$ MLA which has some elusive semantic properties. The canonicity and compactness of the axiom are the problems historically important in the development of our understanding of intensional logic. These problems, however, were unsolved for years in modal logic. Recently, Robert Goldblatt showed that the McKinsey Axiom is not canonical. Then the remaining task is to solve the problem of the compactness of the axiom. The major result in this dissertation is a proof in S 4 showing that the McKinsey Axiom is not compact. The dissertation also contains a variation of Goldblatt's proof and a demonstration that the model constructed by Goldblatt for showing that the McKinsey Axiom is not canonical is not suitable for showing that the McKinsey Axiom is not compact