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A transfer theorem for Henselian valued and ordered fields

Published online by Cambridge University Press:  12 March 2014

Rafel Farré
Rafel Farré*
Affiliation:
Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo, 5, 08028 Barcelona, Spain, E-mail: [email protected]
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Abstract

In well-known papers ([A-K1], [A-K2], and [E]) J. Ax, S. Kochen, and J. Ershov prove a transfer theorem for henselian valued fields. Here we prove an analogue for henselian valued and ordered fields. The orders for which this result apply are the usual orders and also the higher level orders introduced by E. Becker in [Bl] and [B2]. With certain restrictions, two henselian valued and ordered fields are elementarily equivalent if and only if their value groups (with a little bit more structure) and their residually ordered residue fields (a henselian valued and ordered field induces in a natural way an order in its residue field) are elementarily equivalent. Similar results are proved for elementary embeddings and ∀-extensions (extensions where the structure is existentially closed).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 3 , September 1993 , pp. 915 - 930
Copyright
Copyright © Association for Symbolic Logic 1993

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References

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