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Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical Propositional Logics (Trends in Logic, 14) by Silvio Ghilardi, Marek Zawadowski is a nonfiction available to read on EtoBox.

What is Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical Propositional Logics (Trends in Logic, 14) about?

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

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Author

Silvio Ghilardi, Marek Zawadowski

Publisher

Springer-Verlag New York, LLC

Published

2010

Language

EN

ISBN

9789401599368

Category

nonfiction

Subjects

Mathematics, Philosophy, Computer Science