Definable sets in algebraically closed valued fields : elimination of imaginaries

@inproceedings{Haskell2005DefinableSI,
  title={Definable sets in algebraically closed valued fields : elimination of imaginaries},
  author={Deirdre Haskell and Ehud Hrushovski and Dugald Macpherson},
  year={2005}
}
It is shown that if K is an algebraically closed valued field with valuation ring R, then Th(K) has elimination of imaginaries if sorts are added whose elements are certain cosets in K of certain definable R-submodules of K (for all n ≥ 1). The proof involves the development of a theory of independence for unary types, which play the role of 1-types, followed by an analysis of germs of definable functions from unary sets to the sorts.