A Subalgebra Intersection Property for Congruence Distributive Varieties We prove that if a finite algebra $\m a$ generates a congruence distributive variety, then the subalgebras of the powers of $\m a$ satisfy a certain kind of intersection property that fails for finite idempotent algebras that locally exhibit affine or unary behaviour. We demonstrate a connection between this property and the constraint satisfaction problem. Keywords:congruence distributive, constraint satisfaction problem, tame congruence theory, \jon terms, Mal'cev conditionCategories:08B10, 68Q25, 08B05