Logic in Practice: Model-Theoretic Completeness
Model theory is unusual as a field where the abstract and ''impractical" machinery of logic has concrete applications. The abstract quality of logic lends a generality to model theory which is a real asset, allowing a wide range of applications. The only necessary similarity between these areas of application is that the subject matter be characterizable in terms of formal systems of axioms. Since this includes topics from economics to abstract algebra, there is ample reason for an interest in model theory. Model theory is a relatively new field, even in the rapidly expanding discipline of mathematics. The first hints of it appeared in the work of such men as Tarski, Godel, and Lowenheim in the 1930's, and it is only sincec1950 that it has developed into more than a curiosity of mathematical logic. Now, however, it is a much more organized and unified subject which is becoming more and more popular as a tool in numerous theoretical subjects. In a number of cases it has already proven invaluable, and it quite likely to find even wider usefulness due to its powerful generality.