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T-convexity and tame extensions II

Published online by Cambridge University Press:  12 March 2014

Lou van den Dries
Lou van den Dries*
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61820, USA, E-mail: vddries@symcom.math.uiuc.edu
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Extract

I solve here some problems left open in “T-convexity and Tame Extensions” [9]. Familiarity with [9] is assumed, and I will freely use its notations. In particular, T will denote a complete o-minimal theory extending RCF, the theory of real closed fields. Let (, V) ⊨ Tconvex, let = V/m(V) be the residue field, with residue class map x ↦ : V ↦ , and let υ: → Γ be the associated valuation. “Definable” will mean “definable with parameters”. The main goal of this article is to determine the structure induced by (, V) on its residue fieldand on its value group Γ. In [9] we expanded the ordered field to a model of T as follows. Take a tame elementary substructure ′ of such that R′ ⊆ V and R′ maps bijectively onto under the residue class map, and make this bijection into an isomorphism ′ ≌ of T-models. (We showed such ′ exists, and that this gives an expansion of to a T-model that is independent of the choice of ′.).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 1 , March 1997 , pp. 14 - 34
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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