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Sheaves, Games, and Model Completions

Sheaves, Games, and Model Completions


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About the Book

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.


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Product Details
  • ISBN-13: 9789048160365
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: Softcover reprint of hardcover 1st ed. 2002
  • Language: English
  • Returnable: Y
  • Spine Width: 14 mm
  • Weight: 412 gr
  • ISBN-10: 9048160367
  • Publisher Date: 28 Oct 2010
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 245
  • Series Title: Trends in Logic
  • Sub Title: A Categorical Approach to Nonclassical Propositional Logics
  • Width: 156 mm


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