Abstract model theory
Craig G. Fraser · cIRcle (University of British Columbia) · 2010
We define a notion of logic that provides a general framework for the study of extensions of first-order predicate calculus. The concept of partial isomorphism and its relation to infinitary logics are examined. Results on the definability of ordinals establish the setting for our proof of Lindstrom's Theorem: this theorem gives conditions that characterize first-order logic. We then consider the analogues to the general case of the compactness and Lowenheim properties. For a wide class of logics it is shown that interesting connections exist between the analogues of these properties.