The finite representation property fails for composition and intersection
Roger D. Maddux
TL;DR
This paper demonstrates that certain algebraic structures involving binary relations, closed under intersection and composition, cannot always be represented finitely, showing limitations in finite algebraic representations.
Contribution
It provides a counterexample proving the finite representation property fails for algebras closed under intersection and composition.
Findings
Counterexample algebra not isomorphic to any finite set algebra
Finite representation property fails for these algebraic operations
Shows limitations in finite models of relation algebras
Abstract
The title theorem is proved by example: an algebra of binary relations, closed under intersection and composition, that is not isomorphic to any such algebra on a finite set.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topics in Algebra · Logic, programming, and type systems