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Cylindric-like Algebras and Algebraic Logic

  • Book
  • © 2013

Overview

Editors:
  1. Hajnal Andréka

    1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

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  2. Miklós Ferenczi

    1. Department of Algebra, Budapest University of Technology and Economics, Budapest, Hungary

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  3. István Németi

    1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

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  • A tribute to Tarski’s legacy, this volume gives an overview on how a central part of Tarskian algebraic logic developed in the last 30 years
  • Intends to be a continuation of the Henkin-Monk-Tarski monographs
  • Contains 18 survey papers on main achievements and on new research directions in the theory since 1985
  • Gives a glimpse into the state-of-the-art theory of algebras of relations

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

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Table of contents (19 chapters)

  1. Front Matter

    Pages 1-7
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  2. Introduction

    1. Introduction

      • Hajnal Andréka, Miklós Ferenczi, István Németi
      Pages 9-12

  3. Algebraic Notions Applied to Cylindric-Like Algebras

    1. Front Matter

      Pages 13-13
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    2. Reducing First-order Logic to Df3, Free Algebras

      • Hajnal Andréka, István Németi
      Pages 15-35

    3. Varieties of Two-Dimensional Cylindric Algebras

      • Nick Bezhanishvili
      Pages 37-59

    4. Completions and Complete Representations

      • Robin Hirsch, Ian Hodkinson
      Pages 61-89

    5. Amalgamation, Interpolation and Epimorphisms in Algebraic Logic

      • Judit X. Madarász, Tarek Sayed Ahmed
      Pages 91-103

    6. Neat Reducts and Neat Embeddings in Cylindric Algebras

      • Tarek Sayed Ahmed
      Pages 105-131

  5. Notions of Logic Related to Cylindric-Like Algebras

    1. Front Matter

      Pages 183-183
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    2. Representable Cylindric Algebras and Many-Dimensional Modal Logics

      • Agi Kurucz
      Pages 185-203

    3. Completions, Complete Representations and Omitting Types

      • Tarek Sayed Ahmed
      Pages 205-221

    4. Elements of Cylindric Algebraic Model Theory

      • György Serény
      Pages 223-248

    5. Cylindric Modal Logic

      • Yde Venema
      Pages 249-269

  6. Applications of Cylindric-Like Algebras

    1. Front Matter

      Pages 271-271
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    2. Crs and Guarded Logics: A Fruitful Contact

      • Johan Van Benthem
      Pages 273-301

    3. Cylindric Probability Algebras

      • Radosav. S. ĐorĐević, Miodrag. D. Rašković
      Pages 303-320

    4. Cylindric Algebras and Relational Databases

      • Ivo Düntsch
      Pages 321-331
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Keywords

About this book

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.​

Editors and Affiliations

  • Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    Hajnal Andréka, István Németi

  • Department of Algebra, Budapest University of Technology and Economics, Budapest, Hungary

    Miklós Ferenczi

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