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Relative decidability and definability in henselian valued fields

Published online by Cambridge University Press:  12 March 2014

Joseph Flenner
Joseph Flenner*
Affiliation:
University of Notre Dame, Department of Mathematics, 255 Hurley Hall, Notre Dame, IN 46556, USA, E-mail: jflenner@nd.edu
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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.

Keywords

Henselian valued fielddecidabilityquantifier eliminationelimination of imaginaries
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011 , pp. 1240 - 1260
Copyright
Copyright © Association for Symbolic Logic 2011

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