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  1. Tame Properties of Sets and Functions Definable in Weakly o-Minimal Structures.Jafar S. Eivazloo & Somayyeh Tari - 2014 - Archive for Mathematical Logic 53 (3-4):433-447.
    Let M=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}=}$$\end{document} be a weakly o-minimal expansion of a dense linear order without endpoints. Some tame properties of sets and functions definable in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} which hold in o-minimal structures, are examined. One of them is the intermediate value property, say IVP. It is shown that strongly continuous definable functions in M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{M}}}$$\end{document} satisfy an extended (...)
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  • On Definable Skolem Functions in Weakly o-Minimal Nonvaluational Structures.Pantelis E. Eleftheriou, Assaf Hasson & Gil Keren - 2017 - Journal of Symbolic Logic 82 (4):1482-1495.
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  • 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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  • Elimination of Quantifiers for Ordered Valuation Rings.M. A. Dickmann - 1987 - Journal of Symbolic Logic 52 (1):116-128.
  • Paires de Structures o-Minimales.Yerzhan Baisalov & Bruno Poizat - 1998 - Journal of Symbolic Logic 63 (2):570-578.
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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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  • On the Strong Cell Decomposition Property for Weakly o‐Minimal Structures.Roman Wencel - 2013 - Mathematical Logic Quarterly 59 (6):452-470.
  • On Lovely Pairs of Geometric Structures.Alexander Berenstein & Evgueni Vassiliev - 2010 - Annals of Pure and Applied Logic 161 (7):866-878.
    We study the theory of lovely pairs of geometric structures, in particular o-minimal structures. We use the pairs to isolate a class of geometric structures called weakly locally modular which generalizes the class of linear structures in the settings of SU-rank one theories and o-minimal theories. For o-minimal theories, we use the Peterzil–Starchenko trichotomy theorem to characterize for a sufficiently general point, the local geometry around it in terms of the thorn U-rank of its type inside a lovely pair.
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  • A Note on Prime Models in Weakly o-Minimal Structures.Somayyeh Tari - 2017 - Mathematical Logic Quarterly 63 (1-2):109-113.
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  • Tame Topology and O-Minimal Structures.Lou van den Dries - 2000 - Bulletin of Symbolic Logic 6 (2):216-218.