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Cylindric-like Algebras and Algebraic Logic

  • Hajnal Andréka
  • Miklós Ferenczi
  • István Németi

Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 22)

Table of contents

  1. Front Matter
    Pages 1-7
  2. Introduction

    1. Hajnal Andréka, Miklós Ferenczi, István Németi
      Pages 9-12
  3. Algebraic Notions Applied to Cylindric-Like Algebras

    1. Front Matter
      Pages 13-13
    2. Hajnal Andréka, István Németi
      Pages 15-35
    3. Nick Bezhanishvili
      Pages 37-59
    4. Robin Hirsch, Ian Hodkinson
      Pages 61-89
    5. Judit X. Madarász, Tarek Sayed Ahmed
      Pages 91-103
  4. Representation Theory

  5. Notions of Logic Related to Cylindric-Like Algebras

    1. Front Matter
      Pages 183-183
    2. György Serény
      Pages 223-248
    3. Yde Venema
      Pages 249-269
  6. Applications of Cylindric-Like Algebras

    1. Front Matter
      Pages 271-271
    2. Johan Van Benthem
      Pages 273-301
    3. Radosav. S. ĐorĐević, Miodrag. D. Rašković
      Pages 303-320
    4. Ivo Düntsch
      Pages 321-331
  7. Other Algebraic Versions of Logic

    1. Front Matter
      Pages 349-349
    2. Allen L. Mann
      Pages 351-366
    3. Gábor Sági
      Pages 367-389
  8. Connections with Abstract Algebraic Logic and Universal Logic

    1. Front Matter
      Pages 391-391
    2. Ildikó Sain
      Pages 393-419
  9. Back Matter
    Pages 421-478

About this book

Introduction

Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways:  as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.​

Keywords

Algebraic Logic Algebras of Relations Cylindric Algebras Foundation of Mathematics Model Theory Theory Morphisms

Editors and affiliations

  • Hajnal Andréka
    • 1
  • Miklós Ferenczi
    • 2
  • István Németi
    • 1
  1. 1.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  2. 2.Department of AlgebraBudapest University of Technology and EconomicsBudapestHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-35025-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-35024-5
  • Online ISBN 978-3-642-35025-2
  • Series Print ISSN 1217-4696
  • Buy this book on publisher's site