Institution-independent Model Theory

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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.

Author(s): Razvan Diaconescu
Series: Studies in Universal Logic
Edition: 1
Publisher: Birkhäuser Basel
Year: 2008

Language: English
Pages: 377

Cover......Page 1
Preface......Page 7
Contents......Page 9
1. Introduction......Page 12
2. Categories......Page 18
3. Institutions......Page 33
4. Theories and Models......Page 58
5. Internal Logic......Page 99
6. Model Ultraproducts......Page 128
7. Saturated Models......Page 148
8. Preservation and Axiomatizability......Page 169
9. Interpolation......Page 195
10. Definability......Page 228
11. Possible Worlds......Page 239
12. Grothendieck Institutions......Page 256
13. Institutions with Proofs......Page 277
14. Specification......Page 319
15. Logic Programming......Page 338
Appendix A......Page 352
Bibliography......Page 356
Index......Page 369