Prototypes for Definable Subsets of Algebraically Closed Valued Fields
Jan E. Holly
Source: J. Symbolic Logic Volume 62, Issue 4 (1997), 1093-1141.
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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Mathematical Reviews number (MathSciNet):
MR1618005
Zentralblatt MATH identifier:
0899.03027