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Institution-independent model theory

Diaconescu, Răzvan.

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Institution-independent model theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Institution-independent model theory/ by Răzvan Diaconescu.
Author:	Diaconescu, Răzvan.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xiii, 568 p. :ill. (chiefly color), digital ;24 cm.
[NT 15003449]:	- 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.
Contained By:	Springer Nature eBook
Subject:	Model theory. -
Online resource:	https://doi.org/10.1007/978-3-031-68854-6
ISBN:	9783031688546

Institution-independent model theory
Diaconescu, Răzvan.

Institution-independent model theory[electronic resource] /by Răzvan Diaconescu. - Second edition. - Cham :Springer Nature Switzerland :2025. - xiii, 568 p. :ill. (chiefly color), digital ;24 cm. - Studies in universal logic,2297-0290. - Studies in universal logic..

- 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.

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.

ISBN: 9783031688546

Standard No.: 10.1007/978-3-031-68854-6doiSubjects--Topical Terms:

560899
Model theory.

LC Class. No.: QA9.7

Dewey Class. No.: 511.34

Institution-independent model theory
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300 $a xiii, 568 p. : $b ill. (chiefly color), digital ; $c 24 cm.
490 1 $a Studies in universal logic, $x 2297-0290
505 0 $a - 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.
520 $a 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.
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650 1 4 $a Mathematical Logic and Foundations. $3 892656
650 2 4 $a Formal Languages and Automata Theory. $3 3592087
650 2 4 $a Logic. $3 529544
650 2 4 $a Model Theory. $3 3596410
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830 0 $a Studies in universal logic. $3 1619546
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