Some Results On The Subalgebra Intersection Property Arising From Polin Algebras

Abstract

<p>To help answer some questions regarding the complexity classifications of constraint satisfaction problems, Valeriote developed the notion of intersection properties of powers of algebras. Valeriote showed some connections between these intersection properties and the tame congruence theory types of the algebras that satisfy or fail them. This paper uses Polin algebras to refute a conjecture of Valeriote and to motivate further investigation into the connection between intersection properties, tame congruence theory and congruence distributivity.</p>