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Prototypes for definable subsets of algebraically closed valued fields

Published online by Cambridge University Press:  12 March 2014

Jan E. Holly
Jan E. Holly*
Affiliation:
Department of Mathematics and Computer Science, Colby College, Waterville, Me 04901, USA, E-mail: jeholly@colby.edu
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 4 , December 1997 , pp. 1093 - 1141
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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