
Institution-independent Model Theory
Series: Studies in Universal Logic;
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Product details:
- Edition number Second Edition 2025
- Publisher Birkhäuser
- Date of Publication 6 March 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783031688539
- Binding Hardback
- No. of pages568 pages
- Size 235x155 mm
- Language English
- Illustrations 2 Illustrations, color 693
Categories
Short description:
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 general 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 axiomatic top-down methodology allows for a structurally clean understanding of model-theoretic phenomena. Consequently, results from conventional concrete model theory can be understood more easily, and sometimes even new results are obtained. Moreover, all this is also applied to non-classical model theories.
This second edition introduces some novelties in the presentation style which aim to enhance the readability of the material and the proofs. Additional chapters have also been added.
MoreLong description:
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 general 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 axiomatic top-down methodology allows for a structurally clean understanding of model-theoretic phenomena. Consequently, results from conventional concrete model theory can be understood more easily, and sometimes even new results are obtained. Moreover, all this is also applied to non-classical model theories.
This second edition introduces some novelties in the presentation style which aim to enhance the readability of the material and the proofs. Additional chapters have also been added.
MoreTable of Contents:
- Introduction.- Part I Basics.- Categories.- Institutions.- Theories and Models.- Internal Logic.- Part II Advanced Topics.- Model Ultraproducts.- Saturated Models.- Preservation and Axiomatizability.- Interpolation.- Definability.- Part III Extensions.- Institutions with Proofs.- Models with States.- Many-valued Truth Institutions.- Part IV Applications to Computing.- Grothendieck Institutions.- Specification.- Logic Programming.
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