This book develops model theory independently of any concrete logical system or structure, within the abstract category-theoretic framework of the so called 'institution theory'. The concept of institution provides a model theory oriented mathematical formulation for the intuitive concept of logical system andhad arisen within computing science as a response to the population explosionof specification logics. Our development includes most of the important methods and concepts of conventional concrete model theory at the abstract institution-independent level. Consequently it is easily applicable to a diverse rather large collection of logics from the mathematical and computing science practice, many of them not having a proper model theory prior to this work. Moreover the novel top-down methodology proposed leads to an understanding of model theoretic phenomena which is guided by structurally clean causality. Presents anovel approach to model theory beyond any commitement to concrete particular logics. Develops a new top-down methodology for doing model theory leading to important theoretical consequences. Within the rather large institution theoryliterature the first book dedicated to model theory. Gathers together in a unitary way important works in the area published through various journals or even yet unpublished INDICE: 1.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. References. Index.
- ISBN: 978-3-7643-8707-5
- Editorial: Birkhaüser
- Encuadernacion: Rústica
- Páginas: 360
- Fecha Publicación: 01/03/2008
- Nº Volúmenes: 1
- Idioma: Inglés