Sheaves, Games, and Model Completions

A Categorial Approach to Nonclassical Propositional Logics

  • Silvio Ghilardi
  • Marek Zawadowski

Part of the Trends in Logic book series (TREN, volume 14)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Silvio Ghilardi, Marek Zawadowski
    Pages 1-14
  3. Silvio Ghilardi, Marek Zawadowski
    Pages 15-47
  4. Silvio Ghilardi, Marek Zawadowski
    Pages 49-71
  5. Silvio Ghilardi, Marek Zawadowski
    Pages 73-113
  6. Silvio Ghilardi, Marek Zawadowski
    Pages 115-162
  7. Silvio Ghilardi, Marek Zawadowski
    Pages 163-180
  8. Silvio Ghilardi, Marek Zawadowski
    Pages 181-201
  9. Silvio Ghilardi, Marek Zawadowski
    Pages 203-205
  10. Silvio Ghilardi, Marek Zawadowski
    Pages 207-231
  11. Back Matter
    Pages 233-245

About this book


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.


Interpolation logic modal logic model theory proof simulation

Authors and affiliations

  • Silvio Ghilardi
    • 1
  • Marek Zawadowski
    • 2
  1. 1.Università degli Studi di MilanoMilanItaly
  2. 2.Uniwersytet WarszawskiWarsawPoland

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6036-5
  • Online ISBN 978-94-015-9936-8
  • Series Print ISSN 1572-6126
  • Series Online ISSN 2212-7313
  • About this book