Core Concepts
Generalizing cardinality axioms to Stone relation algebras and exploring representability conditions.
Abstract
The study focuses on extending cardinality axioms to Stone relation algebras, emphasizing the representability of these algebras. It delves into the relationships between various axioms for cardinality, aiming to simplify them for relation algebras. The paper provides sufficient conditions for the representability of Stone relation algebras and explores how atoms below an element impact properties. Notably, it presents key results regarding the representation of Stone relation algebras using lattice-valued matrices and discusses simpler formulations of cardinality axioms in atomic Stone relation algebras. Theorems are formally verified in Isabelle/HOL, ensuring accuracy and reliability.
Stats
Every simple and atomic Stone relation algebra with finitely many atoms is a relation algebra (Theorem 12).
Every simple Stone relation algebra with finitely many atoms is a relation algebra (Theorem 13).
Quotes
"Every simple and atomic Stone relation algebra with finitely many atoms is a relation algebra." - Theorem 12.
"Every simple Stone relation algebra with finitely many atoms is a relation algebra." - Theorem 13.