Sheaves, Games, and Model Completions - A Categorical Approach to Nonclassical Propositional Logics (Paperback, Softcover reprint of hardcover 1st ed. 2002)

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."

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Trends in Logic, 14
Release date:	October 2010
First published:	2002
Authors:	Silvio Ghilardi • M. Zawadowski
Dimensions:	240 x 160 x 13mm (L x W x T)
Format:	Paperback
Pages:	245
Edition:	Softcover reprint of hardcover 1st ed. 2002
ISBN-13:	978-90-481-6036-5
Categories:	Books > Humanities > Philosophy > Topics in philosophy > Logic Books > Science & Mathematics > Mathematics > Mathematical foundations > General Books > Science & Mathematics > Mathematics > Algebra > General Books > Computing & IT > Applications of computing > Artificial intelligence > General Books > Philosophy > Topics in philosophy > Logic
LSN:	90-481-6036-7
Barcode:	9789048160365

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