Journal of Symbolic Logic

Prototypes for Definable Subsets of Algebraically Closed Valued Fields

Jan E. Holly

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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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745368

Mathematical Reviews number (MathSciNet)
MR1618005

Zentralblatt MATH identifier
0899.03027

JSTOR
links.jstor.org

Citation

Holly, Jan E. Prototypes for Definable Subsets of Algebraically Closed Valued Fields. J. Symbolic Logic 62 (1997), no. 4, 1093--1141. https://projecteuclid.org/euclid.jsl/1183745368


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