Institution-independent Model Theory / by R?zvan Diaconescu.

Springer eBooks

Categories -- Institutions -- Theories and Models -- Internal Logic -- Model Ultraproducts -- Saturated Models -- Preservation and Axiomatizability -- Interpolation -- Definability -- Possible Worlds -- Grothendieck Institutions -- Institutions with Proofs -- Specification -- Logic Programming.

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.

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