Springer Monographs in Mathematics

Basic Course on Many-Valued Logic and Clone Theory

By: Dietlinde Lau

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Hardcover | 3 August 2006

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688 Pages

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24.13 x 22.23 x 3.18

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Functions which are defined on finite sets occur in almost all fields of mathematics. For more than 80 years algebras whose universes are such functions (so-called function algebras), have been intensively studied.

This book gives a broad introduction to the theory of function algebras and leads to the cutting edge of research. To familiarize the reader from the very beginning on with the algebraic side of function algebras the more general concepts of the Universal Algebra is given in the first part of the book. The second part on fuction algebras covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, clone theory.

This book is an insdispensible source on function algebras for graduate students and researchers in mathematical logic and theoretical computer science.

Industry Reviews

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"'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." (Bela Csakany, Acta Scientiarum Mathematicarum, Vol. 74, 2008)

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You Can Find This Book In

Non-Fiction Mathematics Algebra Mathematical Foundation Mathematical Logic Calculus & Mathematical Analysis Differential Calculus & Equations Computing & I.T.Computer Science Computer Architecture & Logic Design Computer Hardware

Universal algebra
Basic concepts of universal algebra	p. 25
Lattices	p. 35
Hull systems and closure operators	p. 45
Homomorphisms, congruences, and galois connections	p. 51
Direct and subdirect products	p. 61
Varieties, equational classes, and free algebras	p. 71
Function algebras
Basic concepts, notations, and first properties	p. 91
The galois-connection between function- and relation-algebras	p. 125
The subclasses of P[subscript 2]	p. 145
The subclasses of P[subscript k] which contain P[subscript k][superscript 1]	p. 159
The maximal classes of P[subscript k]	p. 163
Rosenberg's completeness criterion for P[subscript k]	p. 191
Further completeness criteria	p. 211
Some properties of the lattice L[subscript k]	p. 219
Congruences and automorphisms on function algebras	p. 233
The relation degree and the dimension of subclasses of P[subscript k]	p. 291
On generating systems and orders of the subclasses of P[subscript k]	p. 307
Subclasses of P[subscript k,2]	p. 335
Classes of linear functions	p. 383
Submaximal classes of P[subscript 3]	p. 399
Finite and countably infinite sublattices of depth 1 or 2 of L[subscript 3]	p. 433
The maximal classes of [actual symbol not reproducible]	p. 499
Maximal classes of Pol[subscript k]E[subscript l] for 2 [actual symbol not reproducible] l < k	p. 515
Further submaximal classes of P[subscript k]	p. 555
Minimal classes and minimal clones of P[subscript k]	p. 589
Partial function algebras	p. 597
Table of Contents provided by Blackwell. All Rights Reserved.

Springer Monographs in Mathematics

Basic Course on Many-Valued Logic and Clone Theory

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

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