 However, because of the second order universal quantification implicit in its semantics, this connective suffices to greatly increase the expressive complexity of the logic: in particular, as shown in (Yang 2013), any sentence of second order logic is equivalent to some sentence of intuitionistic dependence logic. Intuitionistic dependence logic retains the downwards closure property: if a team satisfies an intuitionistic dependence logic formula then so do all of its subsets.