  In this paper, we introduce a logic based on team semantics, called FOT,
whose expressive power is elementary, i.e., coincides with first-order logic
both on the level of sentences and (possibly open) formulas, and we also show
that a sublogic of FOT, called FOT${}^\downarrow$, captures exactly downward
closed elementary (or first-order) team properties. We axiomatize completely
the logic FOT, and also extend the known partial axiomatization of dependence
logic to dependence logic enriched with the logical constants in
FOT${}^\downarrow$.
