  A Basarab-Kuhlmann style language L_RV is introduced in the
Hrushovski-Kazhdan integration theory. The theory ACVF of algebraically closed
valued fields formulated in this language admits quantifier elimination. In
this paper, using well-known facts in the theory of valued fields, we give a
straightforward proof of this fact. We also show that two expansions of ACVF,
one with a section of the entire RV-sort and the other with a section of the
residue field, admit quantifier elimination. Thereafter we show that, in terms
of certain minimality conditions, the three theories are distinct
geometrically.
