Centrala begrepp
Stone relation algebras' cardinality operation generalization and representability conditions are explored.
Sammanfattning
This study delves into the cardinality operation in Stone relation algebras, extending from relation algebras. The research investigates the representation of Stone relation algebras with a cardinality operation. Various axioms for cardinality are discussed, along with their implications on atoms and representability. Key results include sufficient conditions for representability, relationships between cardinality axioms, and the impact of atoms on operations. Theorems provide insights into atomic and simple relation algebras with finite atoms.
Structure:
Introduction to Relation Algebras
Basic Definitions and Properties
Representability of Stone Relation Algebras
Cardinality in Stone Relation Algebras
Further Axioms for Atoms Below an Element
Open Problem and Future Work
Statistik
Previous work has axiomatized the cardinality operation in relation algebras.
Stone relation algebras model weighted graphs.
Every simple Stone relation algebra with finitely many atoms is a relation algebra.
Citat
"Every simple Stone relation algebra with finitely many atoms is a relation algebra." - Theorem 12