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Dries Lou Van Den & H. Lewenberg Adam (1995). T-Convexity and Tame Extensions.

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  1.  3
    Non-Archimedean Stratifications of Tangent Cones.Erick García Ramírez - 2017 - Mathematical Logic Quarterly 63 (3-4):299-312.
    We study the impact of a kind of non-archimedean stratifications on tangent cones of definable sets in real closed fields. We prove that such stratifications induce stratifications of the same nature on the tangent cone of a definable set at a fixed point. As a consequence, the archimedean counterpart of a t-stratification is shown to induce Whitney stratifications on the tangent cones of a semi-algebraic set. Extensions of these results are proposed for real closed fields with further structure.
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    O-Minimal Residue Fields of o-Minimal Fields.Jana Maříková - 2011 - Annals of Pure and Applied Logic 162 (6):457-464.
    Let R be an o-minimal field with a proper convex subring V. We axiomatize the class of all structures such that , the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in Maříková [8] it was shown that certain first-order conditions on are sufficient for the o-minimality of . Here we prove that these conditions are also necessary.
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    Pseudo Completions and Completions in Stages of o-Minimal Structures.Marcus Tressl - 2006 - Archive for Mathematical Logic 45 (8):983-1009.
    For an o-minimal expansion R of a real closed field and a set $\fancyscript{V}$ of Th(R)-convex valuation rings, we construct a “pseudo completion” with respect to $\fancyscript{V}$ . This is an elementary extension S of R generated by all completions of all the residue fields of the $V \in \fancyscript{V}$ , when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings up to an R-isomorphism. For polynomially (...)
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    The Elementary Theory of Dedekind Cuts in Polynomially Bounded Structures.Marcus Tressl - 2005 - Annals of Pure and Applied Logic 135 (1-3):113-134.
    Let M be a polynomially bounded, o-minimal structure with archimedean prime model, for example if M is a real closed field. Let C be a convex and unbounded subset of M. We determine the first order theory of the structure M expanded by the set C. We do this also over any given set of parameters from M, which yields a description of all subsets of Mn, definable in the expanded structure.
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