Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical Propositional Logics - Trends in Logic 14 (Hardback)
  • Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical Propositional Logics - Trends in Logic 14 (Hardback)
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Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical Propositional Logics - Trends in Logic 14 (Hardback)

(author), (author)
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Hardback 245 Pages / Published: 31/07/2002
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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.

Publisher: Springer-Verlag New York Inc.
ISBN: 9781402006609
Number of pages: 245
Weight: 543 g
Dimensions: 235 x 155 x 15 mm
Edition: 2002 ed.

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