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Quantifier elimination in valued Ore modules

Published online by Cambridge University Press:  12 March 2014

Luc Bélair  and
Françoise Point
Luc Bélair
Affiliation:
Département de Mathématiques, Université du Québec-Uqam, Cp. 8888 Succ. Centre-Ville, Montréal, Québec, H3C 3P8, Canada. E-mail: belair.luc@uqam.ca
Françoise Point
Affiliation:
Institut de Mathématique, Université de Möns, Le Pentagone 20, Place du Parc, B-7000 Mons, Belgium. E-mail: point@logique.jussieu.fr
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Abstract

We consider valued fields with a distinguished isometry or contractive derivation as valued modules over the Ore ring of difference operators. Under certain assumptions on the residue field, we prove quantifier elimination first in the pure module language, then in that language augmented with a chain of additive subgroups, and finally in a two-sorted language with a valuation map. We apply quantifier elimination to prove that these structures do not have the independence property.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 3 , September 2010 , pp. 1007 - 1034
Copyright
Copyright © Association for Symbolic Logic 2010

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