Sheaves, Games, and Model Completions: A Categorical Approach to Nonclassical Propositional Logics (2002) (Trends in Logic #14)

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Synopsis
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.
Copyright:
2002

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9789401599368
Related ISBNs:
9781402006609
Publisher:
Springer Netherlands
Date of Addition:
Copyrighted By:
N/A
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
Nonfiction, Computers and Internet, Mathematics and Statistics, Philosophy
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.

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