Corpus ID: 237940170

Un principe d'Ax-Kochen-Ershov imaginaire

  title={Un principe d'Ax-Kochen-Ershov imaginaire},
  author={Martin Hils and Silvain Rideau-Kikuchi},
We study interpretable sets in henselian and σ-henselian valued fields with value group elementarily equivalent to Q or Z. Our first result is an Ax-Kochen-Ershov type principle for weak elimination of imaginaries in finitely ramified characteristic zero henselian fields — relative to value group imaginaries and residual linear imaginaries. We extend this result to the valued difference context and show, in particular, that existentially closed equicharacteristic zero multiplicative difference… Expand


Elimination of imaginaries in multivalued fields
In this paper we study elimination of imaginaries in some classes of henselian valued fields of equicharacteristic zero and residue field algebraically closed. The results are sensitive to theExpand
Imaginaries and invariant types in existentially closed valued differential fields
  • Silvain Rideau
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
  • 2019
We answer three related open questions about the model theory of valued differential fields introduced by Scanlon. We show that they eliminate imaginaries in the geometric language introduced byExpand
  • Silvain Rideau
  • Mathematics
  • Journal of the Institute of Mathematics of Jussieu
  • 2015
We prove field quantifier elimination for valued fields endowed with both an analytic structure that is $\unicode[STIX]{x1D70E}$ -Henselian and an automorphism that is $\unicode[STIX]{x1D70E}$Expand
Definable sets in algebraically closed valued fields: elimination of imaginaries
Abstract It is shown that if K is an algebraically closed valued field with valuation ring R, then Th(K) has elimination of imaginaries if sorts are added whose elements are certain cosets in Kn ofExpand
Quantifier Elimination for the Relative Frobenius
Let (K, v) be a complete discretely valued field of characteristic zero with an algebraically closed residue field of positive characteristic. Let σ : K → K be a continuous automorphism of K inducingExpand
Groupoids, imaginaries and internal covers
Let T be a first-order theory. A correspondence is established between internal covers of models of T and definable groupoids within T. We also consider amalgamations of independent diagrams ofExpand
Imaginaries, invariant types and pseudo \(p\)-adically closed fields
In this paper, we give a very general criterion for elimination of imaginaries using an abstract independent relation. We also study germs of definable functions at certain well-behaved invariantExpand
Imaginaries and definable types in algebraically closed valued fields
The text is based on notes from a class entitled {\em Model Theory of Berkovich Spaces}, given at the Hebrew University in the fall term of 2009, and retains the flavor of class notes. It includes anExpand
Imaginaries in separably closed valued fields
We show that separably closed valued fields of finite imperfection degree (either with lambda-functions or commuting Hasse derivations) eliminate imaginaries in the geometric language. We then useExpand
Imaginaries in real closed valued fields
  • T. Mellor
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 2006
The paper includes a quantifier elimination theorem for real closed valued fields in a language with sorts for the field, value group and residue field and shows elimination of imaginaries for real close valued fields to suitable sorts. Expand