Dietlinde Lau

Function Algebras on Finite Sets (eBook, PDF)

Basic Course on Many-Valued Logic and Clone Theory

• Format: PDF

Produktbeschreibung

Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras. The second part covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, and clone theory.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 670
• Erscheinungstermin: 23. November 2006
• Englisch
• ISBN-13: 9783540360230
• Artikelnr.: 37371473

Inhaltsangabe

Preliminaries.- Preliminaries.- Universal Algebra.- Basic Concepts of Universal Algebra.- Lattices.- Hull Systems and Closure Operators.- Homomorphisms, Congruences, and Galois Connections.- Direct and Subdirect Products.- Varieties, Equational Classes, and Free Algebras.- Function Algebras.- Basic Concepts, Notations, and First Properties.- The Galois-Connection Between Function- and Relation-Algebras.- The Subclasses of P2.- The Subclasses of Pk Which Contain Pk1.- The Maximal Classes of Pk.- Rosenberg's Completeness Criterion for Pk.- Further Completeness Criteria.- Some Properties of the Lattice .- Congruences and Automorphisms on Function Algebras.- The Relation Degree and the Dimension of Subclasses of Pk.- On Generating Systems and Orders of the Subclasses of Pk.- Subclasses of Pk,2.- Classes of Linear Functions.- Submaximal Classes of P3.- Finite and Countably Infinite Sublattices of Depth 1 or 2 of .- The Maximal Classes of ?a?Q Polka for Q Ek.- Maximal Classes of PolkEl for 2 ? l < k.- Further Submaximal Classes of Pk.- Minimal Classes and Minimal Clones of Pk.- Partial Function Algebras.

Rezensionen

From the reviews: "'The aim of the present book is to introduce the reader to the theory of function algebras and to give the latest state of research for some selected fields.' ... This book will be useful for anyone interested in universal algebra and algebraic foundations of many-valued logics." (Béla Csákány, Acta Scientiarum Mathematicarum, Vol. 74, 2008)