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December 2011 Relative decidability and definability in henselian valued fields
Joseph Flenner
J. Symbolic Logic 76(4): 1240-1260 (December 2011). DOI: 10.2178/jsl/1318338847

Abstract

Let (K,v) 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. The main step in obtaining this partition is an answer to the question, given a polynomial f(x)∈ K[x], what is v(f(x))?

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.

Citation

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Joseph Flenner. "Relative decidability and definability in henselian valued fields." J. Symbolic Logic 76 (4) 1240 - 1260, December 2011. https://doi.org/10.2178/jsl/1318338847

Information

Published: December 2011
First available in Project Euclid: 11 October 2011

zbMATH: 1237.03022
MathSciNet: MR2895394
Digital Object Identifier: 10.2178/jsl/1318338847

Subjects:
Primary: 03C60, 12J10
Secondary: 03C10, 12L05

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 4 • December 2011
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