Abstract

My dissertation is a study in free logic, a modification of the classical predicate calculus of mathematical logic that permits denotationless terms and allows models with empty domains of discourse. My principal interest in free logic is that it provides a natural setting within which to formalize theories involving partially defined functions such as 1/x which, as a function on the real numbers, is not defined for x = 0. The dissertation contains the first complete analysis of definitions and definability as these notions pertain to theories formalized in free logic. The definability principles for free logic are derived from two interpolation theorems for free logic which are proved in the dissertation