Some model theory for almost real closed fields

Journal of Symbolic Logic 61 (4):1121-1152 (1996)

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
Keywords Henselian fields   real closed fields   ordered abelian groups   decidability
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DOI 10.2307/2275808
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References found in this work BETA

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
A Transfer Theorem for Henselian Valued and Ordered Fields.Rafel Farré - 1993 - Journal of Symbolic Logic 58 (3):915 - 930.

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Citations of this work BETA

Definable V-Topologies, Henselianity and NIP.Yatir Halevi, Assaf Hasson & Franziska Jahnke - forthcoming - Journal of Mathematical Logic:2050008.

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