Function Algebras on Finite Sets

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.