UPC: 9789048160365 | Trends in Logic: Sheaves Games and Model Completions: A Categorical Approach to Nonclassical Propositional Logics (Paperback)

UPC lookup results for: 9789048160365 | Trends in Logic: Sheaves Games and Model Completions: A Categorical Approach to Nonclassical Propositional Logics (Paperback)

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.