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Simple Relation Algebras

Benefits

  • Introduces new methods for constructing and analyzing simple relation algebras

  • Contains many new results not available elsewhere

  • Features numerous color diagrams to illustrate the main ideas and theorems

  • Engages the reader with numerous examples, exercises, and historical remarks

Book

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Rectangular and Equivalence Semiproducts

    1. Front Matter
      Pages 1-1
    2. Steven Givant, Hajnal Andréka
      Pages 3-37
    3. Steven Givant, Hajnal Andréka
      Pages 39-63
  3. Diagonal Semiproducts, Semipowers, Simple Closures, and Quasi-bijective Relation Algebras

    1. Front Matter
      Pages 65-69
    2. Steven Givant, Hajnal Andréka
      Pages 71-101
    3. Steven Givant, Hajnal Andréka
      Pages 103-131
    4. Steven Givant, Hajnal Andréka
      Pages 133-188
    5. Steven Givant, Hajnal Andréka
      Pages 189-209
  4. Quotient Algebras and Quotient Semiproducts

    1. Front Matter
      Pages 211-216
    2. Steven Givant, Hajnal Andréka
      Pages 217-261
    3. Steven Givant, Hajnal Andréka
      Pages 263-319
    4. Steven Givant, Hajnal Andréka
      Pages 321-406
  5. Insertion Semiproducts and 2–Quasi–Bijective Relation Algebras

    1. Front Matter
      Pages 407-410
    2. Steven Givant, Hajnal Andréka
      Pages 411-481
    3. Steven Givant, Hajnal Andréka
      Pages 483-521
  6. Back Matter
    Pages 523-622

About this book

Introduction

This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics.

The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatment in author Steven Givant’s textbook, Introduction to Relation Algebras (Springer, 2017).

Keywords

Relation algebras Simple relation algebras Semiproducts Semipowers Simple closures Quotient algebras Quotient semiproducts Insertion semiproducts

Authors and affiliations

  1. 1.Department of MathematicsMills CollegeOaklandUSA
  2. 2.Alfréd Rényi Institute of Mathematics Institute of Mathematics Hungarian Academy of SciencesBudapestHungary

About the authors

Steven Givant is a Professor of Mathematics and Computer Science at Mills College, California. As a long-term collaborator of Alfred Tarski—one of the great logicians—Givant has been involved first-hand in the development of the field of relation algebras since the 1970s. His other books include Introduction to Relation Algebras and Advanced Topics in Relation Algebras (Springer, 2017), Duality Theories for Boolean Algebras with Operators (Springer, 2014), Introduction to Boolean Algebras, with Paul Halmos (Springer, 2009), Logic as Algebra, with Paul Halmos (MAA, 1998), and A Formalization of Set Theory without Variables, with Alfred Tarski (AMS, 1987). He was also a coeditor, with Ralph McKenzie, of the collected papers of Alfred Tarski (Birkhäuser, 1986).

Hajnal Andréka is a Professor of Mathematics at the Alfréd Rényi Institute of Mathematics in the Hungarian Academy of Sciences. She has been a prominent figure in the development of relation algebra theory since the 1970s and won the prestigious Alfréd Rényi Prize in 1987. Her other books include Universal Algebraic Logic, with István Németi and Ildikó Sain (Birkhäuser, 2017), Decision Problems for Equational Theories of Relation Algebras, with Steven Givant and István Németi (AMS, 1997), and Cylindric Set Algebras, with Leon Henkin, J. Donald Monk, Alfred Tarski, and István Németi (Springer, 1981).

Bibliographic information

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