%0 Journal Article
%T Quantifier elimination and minimality conditions in algebraically closed valued fields
%A Yimu Yin
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1006.1393v1