Institution-independent Model Theory

Name: Institution-independent Model Theory
Price: 356.62 AUD
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ISBN: 9783031688539

Răzvan Diaconescu

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Hardback

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English

Birkhauser Verlag AG
06 March 2025

Philosophy: logic; Mathematical logic; Mathematical theory of computation

Series: Studies in Universal Logic

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.

By: Răzvan Diaconescu
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: Second Edition 2025
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031688539
ISBN 10: 3031688538
Series: Studies in Universal Logic
Pages: 568
Publication Date: 06 March 2025
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

- 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.

Răzvan Diaconescu is a research professor of mathematics at the Simion Stoilow Institute of Mathematics of the Romanian Academy (IMAR).