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We consider finitary relations (also known as crosses) that are definable viafinite disjunctions of unary relations, i.e. subsets, taken from a fixed finiteparameter set $\Gamma$. We prove that whenever $\Gamma$ contains at least onenon-empty relation distinct from the full carrier set, there is a countablyinfinite number of polymorphism clones determined by relations that aredisjunctively definable from $\Gamma$. Finally, we extend our result tofinitely related polymorphism clones and countably infinite sets $\Gamma$.

The number of clones determined by disjunctions of unary relations