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Preprint Number 221
221. Joseph Flenner
Relative decidability and definability in henselian valued fields
Submission date: 14 October 2009.
Let K be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. Two applications are given: first, a constructive quantifier elimination relative to the leading terms, suggesting a relative decision procedure; second, a presentation of every definable subset of K as the pullback of a definable set in the leading terms subjected to a linear translation.
Mathematics Subject Classification: 03C60; 12J10; 12L05.
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