Prototypes for definable subsets of algebraically closed valued fields

Journal of Symbolic Logic 62 (4):1093-1141 (1997)
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Abstract

Elimination of imaginaries for 1-variable definable equivalence relations is proved for a theory of algebraically closed valued fields with new sorts for the disc spaces. The proof is constructive, and is based upon a new framework for proving elimination of imaginaries, in terms of prototypes which form a canonical family of formulas for defining each set that is definable with parameters. The proof also depends upon the formal development of the tree-like structure of valued fields, in terms of valued trees, and a decomposition of valued trees which is used in the coding of certain sets of discs

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Cell decompositions of C-minimal structures.Deirdre Haskell & Dugald Macpherson - 1994 - Annals of Pure and Applied Logic 66 (2):113-162.
Complete Theories.Robert L. Vaught - 1960 - Journal of Symbolic Logic 25 (2):172-174.

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