Sheaves, Games, and Model Completions : A Categorical Approach to Nonclassical Propositional Logics

Silvio Ghilardi

ISBN 10: 9048160367 / ISBN 13: 9789048160365

Edité par Springer, Springer, 2010

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - This book is an example of fruitful interaction between (non-classical) propo sitionallogics and (classical) model theory which was made possible due to categorical logic. Its main aim consists in investigating the existence of model completions for equational theories arising from propositional logics (such as the theory of Heyting algebras and various kinds of theories related to proposi tional modal logic ). The existence of model-completions turns out to be related to proof-theoretic facts concerning interpretability of second order propositional logic into ordinary propositional logic through the so-called 'Pitts' quantifiers' or 'bisimulation quantifiers'. On the other hand, the book develops a large number of topics concerning the categorical structure of finitely presented al gebras, with related applications to propositional logics, both standard (like Beth's theorems) and new (like effectiveness of internal equivalence relations, projectivity and definability of dual connectives such as difference). A special emphasis is put on sheaf representation, showing that much of the nice categor ical structure of finitely presented algebras is in fact only a restriction of natural structure in sheaves. Applications to the theory of classifying toposes are also covered, yielding new examples. The book has to be considered mainly as a research book, reporting recent and often completely new results in the field; we believe it can also be fruitfully used as a complementary book for graduate courses in categorical and algebraic logic, universal algebra, model theory, and non-classical logics. 1.

N° de réf. du vendeur 9789048160365

Détails bibliographiques

• Titre: Sheaves, Games, and Model Completions : A Categorical Approach to Nonclassical Propositional Logics
• Éditeur: Springer, Springer
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 9048160367
• ISBN à 13 chiffres: 9789048160365
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 240 L x 160 H x 15 P (en millimètres) 240 millimètres de largeur par 160 millimètres de hauteur par 15 millimètres de profondeur
• Poids: 415 grammes

A propos de ce titre

Synopsis

This book is an example of fruitful interaction between (non-classical) propo- sitionallogics and (classical) model theory which was made possible due to categorical logic. Its main aim consists in investigating the existence of model- completions for equational theories arising from propositional logics (such as the theory of Heyting algebras and various kinds of theories related to proposi- tional modal logic ). The existence of model-completions turns out to be related to proof-theoretic facts concerning interpretability of second order propositional logic into ordinary propositional logic through the so-called 'Pitts' quantifiers' or 'bisimulation quantifiers'. On the other hand, the book develops a large number of topics concerning the categorical structure of finitely presented al- gebras, with related applications to propositional logics, both standard (like Beth's theorems) and new (like effectiveness of internal equivalence relations, projectivity and definability of dual connectives such as difference). A special emphasis is put on sheaf representation, showing that much of the nice categor- ical structure of finitely presented algebras is in fact only a restriction of natural structure in sheaves. Applications to the theory of classifying toposes are also covered, yielding new examples. The book has to be considered mainly as a research book, reporting recent and often completely new results in the field; we believe it can also be fruitfully used as a complementary book for graduate courses in categorical and algebraic logic, universal algebra, model theory, and non-classical logics. 1.