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  1. Weakly o-minimal nonvaluational structures.Roman Wencel - 2008 - Annals of Pure and Applied Logic 154 (3):139-162.
    A weakly o-minimal structure image expanding an ordered group is called nonvaluational iff for every cut left angle bracketC,Dright-pointing angle bracket of definable in image, we have that inf{y−x:xset membership, variantC,yset membership, variantD}=0. The study of nonvaluational weakly o-minimal expansions of real closed fields carried out in [D. Macpherson, D. Marker, C. Steinhorn,Weakly o-minimal structures and real closed fields, Trans. Amer. Math. Soc. 352 5435–5483. MR1781273 (2001i:03079] suggests that this class is very close to the class of o-minimal expansions of (...)
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  • Topological properties of sets definable in weakly o-minimal structures.Roman Wencel - 2010 - Journal of Symbolic Logic 75 (3):841-867.
    The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an analogous result from [2] for sets and functions definable in models of weakly o-minimal theories. We pay special attention to large subsets (...)
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  • Dimension of definable sets, algebraic boundedness and Henselian fields.Lou Van den Dries - 1989 - Annals of Pure and Applied Logic 45 (2):189-209.
  • First order topological structures and theories.Anand Pillay - 1987 - Journal of Symbolic Logic 52 (3):763-778.
    In this paper we introduce the notion of a first order topological structure, and consider various possible conditions on the complexity of the definable sets in such a structure, drawing several consequences thereof.Our aim is to develop, for a restricted class of unstable theories, results analogous to those for stable theories. The “material basis” for such an endeavor is the analogy between the field of real numbers and the field of complex numbers, the former being a “nicely behaved” unstable structure (...)
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