Sheaves, Games, and Model Completions
Subtitle: A Categorial Approach to Nonclassical Propositional Logics
By: by Silvio Ghilardi, Marek Zawadowski
Contributors: Zawadowski, Marek
Series: Trends in Logic, Studia Logica Library -- 14; Trends in Logic, Studia Logica Library -- 14
Publisher: Springer Netherlands
Published: 2002
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 245
ISBN-13: 9789048160365; 9789401599368
Subjects: Philosophy (General); Logic; Symbolic and mathematical Logic; Artificial intelligence; Algebra
Description: This book investigates propositional intuitionistic and modal logics from an entirely new point of view, covering quite recent and sometimes yet unpublished results. It mainly deals with the structure of the category of finitely presented Heyting and modal algebras, relating it both with proof theoretic and model theoretic facts: existence of model completions, amalgamability, Beth definability, interpretability of second order quantifiers and uniform interpolation, definability of dual connectives like difference, projectivity, etc. are among the numerous topics which are covered. Dualities and sheaf representations are the main techniques in the book, together with Ehrenfeucht-Fraissé games and bounded bisimulations. The categorical instruments employed are rich, but a specific extended Appendix explains to the reader all concepts used in the text, starting from the very basic definitions to what is needed from topos theory. Audience: The book is addressed to a large spectrum of professional logicians, from such different areas as modal logics, categorical and algebraic logic, model theory and universal algebra.
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Table of contents: title: 1. Introduction; title: 2. Preliminary Notions; title: 3. Model Completions; title: 4. Heyting Algebras; title: 5. Duality for Modal Algebras; title: 6. Model Completions in Modal Logic; title: 7. Algebraically Closed Models; title: 8. Open Problems; title: 9. Appendix. References; title: Glossary of Notation; title: Subject Index.