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  1.  14
    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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  2.  5
    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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  3.  2
    Strong cell decomposition property in o-minimal traces.Somayyeh Tari - forthcoming - Archive for Mathematical Logic:1-10.
    Strong cell decomposition property has been proved in non-valuational weakly o-minimal expansions of ordered groups. In this note, we show that all o-minimal traces have strong cell decomposition property. Also after introducing the notion of irrational nonvaluational cut in arbitrary o-minimal structures, we show that every expansion of o-minimal structures by irrational nonvaluational cuts is an o-minimal trace.
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  4.  23
    SCE-Cell Decomposition and OCP in Weakly O-Minimal Structures.Jafar S. Eivazloo & Somayyeh Tari - 2016 - Notre Dame Journal of Formal Logic 57 (3):399-410.
    Continuous extension cell decomposition in o-minimal structures was introduced by Simon Andrews to establish the open cell property in those structures. Here, we define strong $\mathrm{CE}$-cells in weakly o-minimal structures, and prove that every weakly o-minimal structure with strong cell decomposition has $\mathrm{SCE}$-cell decomposition if and only if its canonical o-minimal extension has $\mathrm{CE}$-cell decomposition. Then, we show that every weakly o-minimal structure with $\mathrm{SCE}$-cell decomposition satisfies $\mathrm{OCP}$. Our last result implies that every o-minimal structure in which every definable open (...)
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    CE-Cell Decomposition and Open Cell Property in o-Minimal Structures.Somayyeh Tari - 2017 - Annals of Pure and Applied Logic 168 (8):1564-1570.
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