Cylindric-like Algebras and Algebraic Logic

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

4. Representation Theory

   1. Front Matter

      Pages 133-133

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   2. A New Representation Theory: Representing Cylindric-like Algebras by Relativized Set Algebras

      • Miklós Ferenczi*

      Pages 135-162

   3. Representing all Cylindric Algebras by Twisting on a Problem of Henkin

      • András Simon

      Pages 163-182

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

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.​

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

• 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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