Function Algebras on Finite Sets A Basic Course on Many-Valued Logic and Clone Theory /

• Κύριος συγγραφέας: Lau, Dietlinde (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Σειρά: Springer Monographs in Mathematics,
• Θέματα: Mathematics.; Arithmetic and logic units, Computer.; Algebra.; Mathematical logic.; Mathematical Logic and Foundations.; Arithmetic and Logic Structures.

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...

Πίνακας περιεχομένων:

• 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.