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In Team Semantics, a dependency notion is strongly first order if everysentence of the logic obtained by adding the corresponding atoms to First OrderLogic is equivalent to some first order sentence. In this work it is shown thatall nontrivial dependency atoms that are strongly first order, downwardsclosed, and relativizable (in the sense that the relativizations of thecorresponding atoms with respect to some unary predicate are expressible interms of them) are definable in terms of constancy atoms.  Additionally, it is shown that any strongly first order dependency is safefor any family of downwards closed dependencies, in the sense that everysentence of the logic obtained by adding to First Order Logic both the stronglyfirst order dependency and the downwards closed dependencies is equivalent tosome sentence of the logic obtained by adding only the downwards closeddependencies.

Characterizing downwards closed, strongly first order, relativizable dependencies