Ehrenfeucht–Fraïssé games in finite set theory

In this article, with Ehrenfeucht–Fraïssé games we prove that Δ1≠Δ0 on BFR, which implies Δ≠Δ0 on BFR, and thus solve an open problem raised by Albert Atserias in his dissertation (Δ0,Δ1,Δ are fragments of first order logic and BFR is a class of finite sets which in essence is equivalent to a class of finite pure arithmetic structures with built-in BIT predicate).