Institution-independent Model Theory

The Author presents a novel approach to model theory beyond any commitment to concrete particular logics. A model theory that is independent of any concrete logical system allows a general handling of a large variety of logics. This generality can be achieved by applying the theory of institutions that provides a precise mathematical formulation for the intuitive concept of a logical system. Especially in computer science, where the development of a huge number of specification logics is observable, institution-independent model theory simplifies and sometimes even enables a concise model-theoretic analysis of the system. Besides incorporating important methods and concepts from conventional model theory, the proposed top-down methodology allows for a structurally clean understanding of model-theoretic phenomena. As a consequence, results from conventional concrete model theory can be understood more easily, and sometimes even new results are obtained. – 1. Introduction; – 2. Categories; – 3. Institutions; – 4. Theories and Models; – 5. Internal Logic; – 6. Model Ultraproducts; – 7. Saturated Models; – 8. Preservation and Axiomatizability; – 9. Interpolation; – 10. Definability; – 11. Possible Worlds; – 12. Grothendieck Institutions; – 13. Institutions with Proofs; – 14. Specification; – 15. Logic Programming. M.-M. V.