Citations of work:

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

4 found
Order:
Are we missing citations?

PhilPapers citations & references are currently in beta testing. We expect to add many more in the future.

Meanwhile, you can use our bibliography tool to import references for this or another work.

Or you can directly add citations for the above work:

Search for work by author name and title
Add directly by record ID

  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.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  2.  2
    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.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  3.  25
    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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  4.  1
    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.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   1 citation