Function Algebras on Finite Sets

A Basic Course on Many-Valued Logic and Clone Theory

Authors:

ISBN: 978-3-540-36022-3 (Print) 978-3-540-36023-0 (Online)

Table of contents (28 chapters)

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  1. Introduction

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      Pages 1-16

      Introduction

  2. Preliminaries

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      Pages 17-19

      Preliminaries

  3. Universal Algebra

    1. Front Matter

      Pages 21-23

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      Pages 25-33

      Basic Concepts of Universal Algebra

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      Pages 35-44

      Lattices

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      Pages 45-49

      Hull Systems and Closure Operators

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      Pages 51-60

      Homomorphisms, Congruences, and Galois Connections

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      Pages 61-69

      Direct and Subdirect Products

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      Pages 71-88

      Varieties, Equational Classes, and Free Algebras

  4. Function Algebras

    1. Front Matter

      Pages 89-89

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      Pages 91-123

      Basic Concepts, Notations, and First Properties

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      Pages 125-143

      The Galois-Connection Between Function- and Relation-Algebras

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      Pages 145-157

      The Subclasses of P 2

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      Pages 159-162

      The Subclasses of P k Which Contain P k 1

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      Pages 163-190

      The Maximal Classes of P k

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      Pages 191-210

      Rosenberg’s Completeness Criterion for P k

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      Pages 211-218

      Further Completeness Criteria

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      Book Chapter

      Pages 219-232

      Some Properties of the Lattice $ \mathbb{L}_k $

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      Pages 233-290

      Congruences and Automorphisms on Function Algebras

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      Book Chapter

      Pages 291-306

      The Relation Degree and the Dimension of Subclasses of P k

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      Book Chapter

      Pages 307-334

      On Generating Systems and Orders of the Subclasses of P k

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      Book Chapter

      Pages 335-381

      Subclasses of P k,2

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