## Journal of Symbolic Logic

### Some Model Theory for Almost Real Closed Fields

#### Abstract

We study the model theory of fields $k$ carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian group and prove that the definable real valuation rings of $k$ are in correspondence with the definable convex subgroups of the value group of a certain real valuation of $k$.

#### Article information

Source
J. Symbolic Logic, Volume 61, Issue 4 (1996), 1121-1152.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745127

Mathematical Reviews number (MathSciNet)
MR1456099

Zentralblatt MATH identifier
0874.03045

JSTOR