On Strongly First-Order Dependencies
  We prove that the expressive power of first-order logic with team semantics plus contradictory negation does not rise beyond that of first-order logic (with respect to sentences), and that the totality atoms of arity k +1 are not definable in terms of the totality atoms of arity k. We furthermore prove that all first-order nullary and unary dependencies are strongly first order, in the sense that they do not increase the expressive power of first order logic if added to it. 
Pietro Galliani
math.LO cs.LO