Journal of Symbolic Logic

Quantifier elimination in valued Ore modules

Luc Bélair and Françoise Point

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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.

Article information

J. Symbolic Logic, Volume 75, Issue 3 (2010), 1007-1034.

First available in Project Euclid: 9 July 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] 03C10: Quantifier elimination, model completeness and related topics 16D 16S36: Ordinary and skew polynomial rings and semigroup rings [See also 20M25] 12J10: Valued fields


Bélair, Luc; Point, Françoise. Quantifier elimination in valued Ore modules. J. Symbolic Logic 75 (2010), no. 3, 1007--1034. doi:10.2178/jsl/1278682213.

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