Prototypes for definable subsets of algebraically closed valued fields
Journal of Symbolic Logic 62 (4):1093-1141 (1997)
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 discsDOI
10.2307/2275629
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Citations of this work
Relative decidability and definability in henselian valued fields.Joseph Flenner - 2011 - Journal of Symbolic Logic 76 (4):1240-1260.
References found in this work
Cell decompositions of C-minimal structures.Deirdre Haskell & Dugald Macpherson - 1994 - Annals of Pure and Applied Logic 66 (2):113-162.
On the elimination of imaginaries from certain valued fields.Philip Scowcroft & Angus Macintyre - 1993 - Annals of Pure and Applied Logic 61 (3):241-276.