Journal of Symbolic Logic

Prototypes for Definable Subsets of Algebraically Closed Valued Fields

Jan E. Holly

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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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J. Symbolic Logic, Volume 62, Issue 4 (1997), 1093-1141.

First available in Project Euclid: 6 July 2007

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Holly, Jan E. Prototypes for Definable Subsets of Algebraically Closed Valued Fields. J. Symbolic Logic 62 (1997), no. 4, 1093--1141.

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