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＜電子ブック＞
Sheaves, Games, and Model Completions : A Categorical Approach to Nonclassical Propositional Logics / by Silvio Ghilardi, M. Zawadowski
(Trends in Logic, Studia Logica Library. ISSN:22127313 ; 14)

版	1st ed. 2002.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	IX, 245 p : online resource
著者標目	*Ghilardi, Silvio author Zawadowski, M author SpringerLink (Online service)
件　名	LCSH:Logic LCSH:Algebra, Homological LCSH:Algebra LCSH:Mathematical logic LCSH:Artificial intelligence FREE:Logic FREE:Category Theory, Homological Algebra FREE:Order, Lattices, Ordered Algebraic Structures FREE:Mathematical Logic and Foundations FREE:Artificial Intelligence
一般注記	1. Introduction -- 2. Preliminary Notions -- 3. Model Completions -- 4. Heyting Algebras -- 5. Duality for Modal Algebras -- 6. Model Completions in Modal Logic -- 7. Algebraically Closed Models -- 8. Open Problems -- 9. Appendix -- References -- Glossary of Notation 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 HTTP:URL=https://doi.org/10.1007/978-94-015-9936-8

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