Research Catalog

Title

Sheaves, games, and model completions : a categorical approach to nonclassical propositional logics / Silvio Ghilardi, Marek Zawadowski.

Author

Ghilardi, Silvio.

Publication

Dordrecht ; Boston : Kluwer Academic Publishers, ©2002.

Items in the Library & Off-site

Details

Additional Authors

Zawadowski, Marek.

Description

ix, 243 p.; 25 cm.

Summary

"Audience: The book is addressed to a large spectrum of professional logicians, coming from quite different areas such as modal logics, categorical and algebraic logic, model theory and universal algebra."--Jacket.

Series Statement

Trends in logic ; v. 14

Uniform Title

Trends in logic ; v. 14.

Subject

• Categories (Mathematics)
• Proposition (Logic)
• Model theory
• Schoven (Topologie)
• Speltheorie
• Logica
• Categorieën (wiskunde)
• Modeltheorie

Bibliography (note)

• Includes bibliographical references (p. 233-236) and index.

Contents

Motivating example -- An overview of the book -- How to read the book -- Historical remarks -- Preliminary Notions -- Basic algebraic structures -- Model theoretic background -- Subobjects and regular subobjects -- Finitely presented algebras -- Principal congruences -- The amalgamation property -- Model Completions -- r-Heyting categories -- Model completions and fp algebras -- Heyting Algebras -- Finitely presented Heyting algebras -- Duality for Heyting algebras -- A combinatorial result -- Properties of M[subscript H] and [psi subscript H] -- Second order extensions of IpC -- Quantifier-elimination -- M[subscript H] is not exact -- Some applications -- Projective Heyting algebras -- Duality for Modal Algebras -- Frames, evaluations and games -- The category of finite S-frames -- The category M[subscript S] -- Finitely presented S-algebras -- Duality -- Regularity of monomorphisms -- Combinatorial Conditions -- Model Completions in Modal Logic -- Negative results -- Diagonalizable algebras -- Varieties of interior algebras -- Algebraically Closed Models -- FLEA's -- Grothendieck Topologies on algebras -- Sh(T[superscript f], J[superscript f]) as a classifying topos -- Models in Set -- The case of Heyting algebras -- Existentially closed algebras -- Open Problems -- Glossary of basic categorical notions -- Internal algebras in categories -- Grothendieck topologies -- Sheaves -- Associated sheaf functor -- Properties of Grothendieck toposes -- Classifying toposes.

ISBN

• 1402006608
• 9781402006609

LCCN

2002073164

OCLC

• ocm50164819
• 50164819
• SCSB-1353595

Owning Institutions

Princeton University Library