## Journal of Symbolic Logic

### A Transfer Theorem for Henselian Valued and Ordered Fields

Rafel Farre

#### 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 [B1] 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 $\forall$-extensions (extensions where the structure is existentially closed).

#### Article information

Source
J. Symbolic Logic, Volume 58, Issue 3 (1993), 915-930.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744305

Mathematical Reviews number (MathSciNet)
MR1242046

Zentralblatt MATH identifier
0805.12004

JSTOR